Awesome AI for Physics

💥 News

Coming Soon: An AI4Physics survey is currently in development. Stay tuned! 📢

📖 Content

1. Physical Perception

1.1 Object Recognition

1.2 Spatial Perception

1.3 Identifying Intrinsic Property

1.4 Dynamic Estimation

1.5 Causal and Counterfactual Inference

I-PHYRE: Interactive Physical Reasoning

Date: 2023.12
Description: I-PHYRE is a benchmark that evaluates an agent's physical reasoning by requiring it to actively interact with an environment to uncover latent physical properties and solve tasks that are impossible to complete from passive observation alone. It contains 40 interactive physics games mainly consisting of gray blocks, black blocks, blue blocks, and red balls.
Link: https://lishiqianhugh.github.io/IPHYRE/
Domain: Interactive Reasoning Embodied AI

ContPhy: Continuum Physical Concept Learning and Reasoning from Videos

Date: 2024.02
Description: A novel benchmark dataset of videos is designed to evaluate the physical reasoning capabilities of AI models on continuum substances, such as fluids and soft bodies, by requiring them to infer physical properties and predict dynamics in diverse and complex scenarios.
Link: https://physical-reasoning-project.github.io/
Domain: Video Understanding Continuum Mechanics

GRASP: A novel benchmark for evaluating language GRounding And Situated Physics understanding in multimodal language models

Date: 2023.11
Description: A novel benchmark is built in a Unity-based simulation to evaluate how well video-based multimodal large language models can ground language in visual scenes and understand intuitive physics principles like object permanence and solidity.
Link: https://github.com/i-machine-think/grasp
Domain: Video Understanding MLLM

IntPhys 2: Benchmarking Intuitive Physics Understanding In Complex Synthetic Environments

Date: 2025.06
Description: IntPhys 2 is a large-scale benchmark that evaluates the intuitive physics understanding of AI models by challenging them to identify physically impossible events within complex, diverse, and realistic synthetic video scenes.
Link: https://github.com/facebookresearch/IntPhys2
Domain: Video Understanding World Model

LLMPhy: Complex Physical Reasoning Using Large Language Models and World Models

Date: 2024.11
Description: LLMPhy is a zero-shot framework that synergizes the program synthesis abilities of Large Language Models with the simulation power of physics engines to solve complex physical reasoning tasks by iteratively estimating system parameters and predicting object dynamics.
Link:
Domain: Video Understanding World Model LLM

PhysBench: Benchmarking and Enhancing Vision-Language Models for Physical World Understanding

Date: 2025.01
Description: PhysBench, a comprehensive benchmark with 10,002 entries, evaluates physical world understanding across 75 top Vision-Language Models, revealing their struggles with physics and introducing the PhysAgent framework to address this, which improves GPT-4o's performance by 18.4%.
Link: https://physbench.github.io/
Domain: Embodied AI VLM

Physion++: Evaluating Physical Scene Understanding that Requires Online Inference of Different Physical Properties

Date: 2023.06
Description: Physion++ is a novel benchmark that evaluates visual physical prediction models on their ability to perform online inference of latent properties like mass and friction from object dynamics, revealing a huge performance gap between current models and humans.
Link: https://dingmyu.github.io/physion_v2/
Domain: Online Inference

2. Physics Reasoning

2.1 Database (Dataset and benchmarks)

SeePhys: Does Seeing Help Thinking? -- Benchmarking Vision-Based Physics Reasoning

Date: 2025.05
Description: It comprises 2,000 rigorously validated questions covering a comprehensive range of knowledge levels from middle school to PhD qualifying exam levels.Through meticulous selection of 21 diagram types by domain experts, each problem challenges frontier MLLMs to integrate domain knowledge with visual understanding of physics diagrams (e.g., Feynman diagrams for particle interactions and Circuit diagrams for Electromagnetism).
Link: https://seephys.github.io/
Domain: MLLM Physics VQA

PHYSICSEVAL: Inference-Time Techniques to Improve the Reasoning Proficiency of Large Language Models on Physics Problems

Date: 2025.08
Description: A new 19,609-problem physics benchmark, reveals that multi-agent verification frameworks enhance LLM performance on complex physics reasoning tasks.
Link: https://github.com/areebuzair/PhysicsEval
Domain: LLM Physics VQA

ABench-Physics: Benchmarking Physical Reasoning in LLMs via High-Difficulty and Dynamic Physics Problems

Date: 2025.07
Description: ABench-Physics exposes LLMs' physics reasoning limitations through 500 challenging problems (400 static + 100 dynamic variants).
Link: https://github.com/inclusionAI/ABench/tree/main/Physics
Domain: LLM Physics VQA

ScienceAgentBench: Toward Rigorous Assessment of Language Agents for Data-Driven Scientific Discovery

Date: 2024.10
Description: ScienceAgentBench evaluates LLM agents on 102 validated scientific tasks, showing even top-performing models (32.4-42.2% success rates) remain far from reliable automation, with performance gains requiring prohibitive cost increases.
Link: https://osu-nlp-group.github.io/ScienceAgentBench/
Domain: Agent Computational Physics

SciCode: A Research Coding Benchmark Curated by Scientists:

Date: 2024.04
Description: A scientist-curated benchmark (338 subproblems from 80 research challenges) with coding components.
Link: https://scicode-bench.github.io/
Domain: LLM Computational Physics

PhySense: Principle-Based Physics Reasoning Benchmarking for Large Language Models

Date: 2025.05
Description: This paper introduces PhySense, a novel benchmark designed to evaluate the physics reasoning capabilities of Large Language Models (LLMs) based on core principles. The authors find that current LLMs often fail to emulate the concise, principle-based reasoning characteristic of human experts, instead generating lengthy and opaque solutions. PhySense provides a systematic way to investigate this limitation, aiming to guide the development of AI systems with more efficient, robust, and interpretable scientific reasoning.
Domain: Large Language Models AI for Science Physics Reasoning Benchmarking Explainable AI

2.2 General Physics Reasoning Models

2.3 Theoretical Physics Solvers

3. World Model

3.1 Generative Models

PBR-NeRF: Inverse Rendering with Physics-Based Neural Fields

Date: 2024.12
Description: A physics-aware NeRF that jointly recovers shape, materials and lighting via two novel PBR priors, achieving state-of-the-art material accuracy without hurting view synthesis.
Domain: Generation Physics-Based Rendering

IntrinsicAvatar: Physically Based Inverse Rendering of Dynamic Humans from Monocular Videos via Explicit Ray Tracing

Date: 2023.12
Description: IntrinsicAvatar, a novel method for recovering the intrinsic properties of clothed human avatars, including geometry, albedo, material, and ambient lighting, from monocular video alone. Recent advances in eye-based neural rendering have enabled high-quality reconstruction of clothed human geometry and appearance from monocular video alone.
Domain: Reconstruction Ray Tracing

Generative AI for Validating Physics Laws

Date: 2025.03
Description: A generative artificial intelligence (AI) approach was proposed to empirically verify fundamental laws of physics, focusing on the Stefan-Boltzmann law linking stellar temperature and luminosity. The approach simulates the counterfactual luminosity of each star under hypothetical temperature conditions and iteratively refines the temperature-luminosity relationship within a deep learning architecture.
Domain: Generation Astrophysics

Morpheus: Benchmarking Physical Reasoning of Video Generative Models with Real Physical Experiments

Date: 2025.04
Description: Morpheus is a benchmark designed to evaluate the physical reasoning of video generative models, consisting of 80 meticulously filmed real-world videos that capture phenomena governed by physical conservation laws (like the conservation of energy and momentum).
Link: https://physics-from-video.github.io/morpheus-bench/
Domain: Video Generation World Model

T2VPhysBench: A First-Principles Benchmark for Physical Consistency in Text-to-Video Generation

Date: 2025.05
Description: T2VPhysBench is a first-principles benchmark that uses rigorous human evaluation to assess text-to-video models on twelve core physical laws, revealing that all models perform poorly (scoring below 0.60) and consistently fail to generate physically plausible content even when given explicit hints.
Link:
Domain: T2V First-Principles

VideoPhy: Evaluating Physical Commonsense for Video Generation

Date: 2024.06
Description: VideoPhy is a benchmark designed to assess the physical commonsense of text-to-video models using diverse material interaction prompts, revealing through human evaluation that even the best-performing model, CogVideoX-5B, generates videos that are both text-adherent and physically plausible only 39.6% of the time.
Link: https://videophy2.github.io/
Domain: T2V World Simulation

VideoPhy-2: A Challenging Action-Centric Physical Commonsense Evaluation in Video Generation

Date: 2025.03
Description: VideoPhy-2 is a challenging, action-centric benchmark that uses human evaluation to assess physical commonsense in video generation, revealing that even the best models achieve only 22% joint semantic and physical accuracy on its hard subset, particularly struggling with conservation laws.
Link: https://videophy2.github.io/
Domain: Video Generation

3.2 Physics and Physical Engine

Brax: Massively Parallel Rigidbody Physics Simulation on Accelerator Hardware

Date: 2021.06
Description: Brax is a high-performance differentiable physics engine designed for large-scale rigid body simulation and reinforcement learning research in robotics and control tasks.
Domain: Physics Engine Rigid Body Dynamics Differentiable Simulation RL Environment JAX-based Acceleration

Isaac Sim: Robotics Simulation and Synthetic Data Generation

Date: 2020.12
Description: MuJoCo (Multi-Joint dynamics with Contact) is a fast and accurate physics engine designed for model-based optimization and reinforcement learning, featuring efficient contact dynamics and generalized coordinate representation.
Domain: Robotics Simulation Photorealistic Rendering Synthetic Data Generation Digital Twin GPU-Accelerated Physics

MuJoCo: Advanced Physics Simulation

Date: 2012.10
Description: Brax is a high-performance differentiable physics engine designed for large-scale rigid body simulation and reinforcement learning research in robotics and control tasks.
Domain: Contact Dynamics Model-Based Control Continuous Control Constraint-Based Simulation Robotics Research

PyBullet: Time Physics Simulation

Date: 2016.09
Description: PyBullet is a Python interface for the Bullet Physics SDK, providing real-time collision detection, rigid body and soft body dynamics, and robotics simulation with support for various file formats (URDF, SDF, MJCF).
Domain: Collision Detection Rigid and Soft Body Dynamics Robot Simulation Real-Time Physics Open-Source Engine

3.3 Physics-enhanced Modeling Approaches.

GAIA-1: A Generative World Model for Autonomous Driving

Date: 2023.09
Description: GAIA-1 is a generative world model for autonomous driving that generates realistic driving videos conditioned on text, image, and action inputs, enabling controllable prediction of future driving scenarios.
Domain: Autonomous Driving World Simulation

Back to the Features: DINO as a Foundation for Video World Models

Date: 2024.08
Description: DINO-World leverages visual foundation models to build world models for autonomous driving, demonstrating that pre-trained vision transformers can effectively predict future driving scenes and agent behaviors with improved spatial understanding.
Domain: Autonomous Driving World Models

Building World Models with Neural Physics

Date: 2024.08
Description: This work proposes a framework for building world models that incorporate neural physics engines, enabling more accurate prediction of physical interactions and dynamics in video generation by learning physics-based representations.
Domain: World Models Physical Simulation

PhysORD: A Neuro-Symbolic Approach for Physics-infused Motion Prediction in Off-road Driving

Date: 2024.10
Description: A physics-infused world model for off-road driving that integrates the Euler-Lagrange equation with neural networks, achieving 46.7% higher accuracy using only 3.1% of parameters compared to purely data-driven approaches.
Domain: World Models Physics-Informed Learning

Neural Motion Simulator Pushing the Limit of World Models in Reinforcement Learning

Date: 2025.04
Description: MoSim is a neural motion simulator that predicts future physical states of embodied systems using rigid-body dynamics and Neural ODEs, achieving state-of-the-art long-horizon prediction accuracy and enabling zero-shot reinforcement learning.
Domain: Reinforcement Learning World Models

FusionForce: End-to-end Differentiable Neural-Symbolic Layer for Trajectory Prediction

Date: 2025.06
Description: A differentiable world model that fuses camera and lidar data with a physics engine for off-road trajectory prediction, achieving 10^4 trajectories per second with superior out-of-distribution generalization.
Domain: World Models Physics-Informed Learning Off-road Autonomy

3.4 Benchmarking Modeling Capability

GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium

Date: 2017.06
Description: FID is a metric for evaluating GAN-generated image quality by computing the Fréchet distance between feature distributions of real and generated images extracted from Inception-v3. Lower scores indicate better quality and diversity.
Domain: Image Generation GAN Evaluation Generative Models

CLIPScore: A Reference-free Evaluation Metric for Image Captioning

Date: 2021.04
Description: CLIPScore is a reference-free metric that evaluates image captioning quality by computing cosine similarity between CLIP embeddings of images and captions. It achieves higher correlation with human judgments than reference-based metrics like CIDEr and SPICE.
Domain: Image Captioning Evaluation Metrics Vision-Language Models

ImageNet: A Large-Scale Hierarchical Image Database

Date: 2009.06
Description: ImageNet is a large-scale hierarchical image database organized by WordNet structure, containing millions of labeled images across thousands of categories for visual object recognition research.
Domain: Computer Vision Object Recognition

The Kinetics Human Action Video Dataset

Date: 2017.05
Description: Kinetics-400 is a large-scale human action video dataset containing 400 action classes with at least 400 clips per class. Each clip lasts around 10 seconds from YouTube videos, covering human-object and human-human interactions.
Domain: Action Recognition Video Understanding Dataset

Progressive Growing of GANs for Improved Quality, Stability, and Variation

Date: 2017.10
Description: CelebA-HQ is a high-quality version of the CelebA dataset containing 30,000 face images at 1024×1024 resolution, created by selecting and post-processing images from the original CelebA dataset.
Domain: Image Synthesis Dataset

UCF101: A Dataset of 101 Human Actions Classes From Videos in The Wild

Date: 2012.12
Description: UCF101 is an action recognition dataset containing 13,320 realistic video clips from YouTube across 101 action categories, totaling 27 hours of video with diverse camera motions and cluttered backgrounds.
Domain: Action Recognition Video Understanding Dataset

The "Something Something" Video Database for Learning and Evaluating Visual Common Sense

Date: 2017.06
Description: Something-Something is a crowdsourced video dataset containing 100,000+ videos across 174 action classes focused on fine-grained human-object interactions requiring common sense understanding of the physical world.
Domain: Action Recognition Video Understanding Dataset

Unsupervised Learning of Video Representations using LSTMs

Date: 2015.02
Description: Moving MNIST is a video prediction dataset containing 10,000 sequences of 20 frames at 64×64 resolution, showing two handwritten MNIST digits moving and bouncing within the frame.
Domain: Video Prediction Dataset

Self-Supervised Visual Planning with Temporal Skip Connections

Date: 2017.10
Description: BAIR Robot Pushing dataset contains approximately 44,000 video sequences at 64×64 resolution showing a robotic arm pushing various objects, used for video prediction and robotic manipulation tasks.
Domain: Video Prediction Robot Manipulation Dataset

Indoor segmentation and support inference from RGBD images

Date: 2012
Description: NYU-Depth-V2 is an RGB-D indoor scene dataset containing 1,449 densely labeled aligned RGB and depth image pairs captured from 464 diverse indoor scenes across 3 cities using Microsoft Kinect.
Domain: Indoor Scene Understanding Dataset

CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning

Date: 2016.12
Description: CLEVR is a synthetic visual question answering dataset containing 3D-rendered object images with 70,000 training and 15,000 validation images, featuring compositional questions testing visual reasoning abilities like counting, comparison, and spatial relationships.
Domain: Visual Question Answering Visual Reasoning Dataset

4. Embodied Interaction

4.1 Robotics

PhyBlock: A Progressive Benchmark for Physical Understanding and Planning via 3D Block Assembly

Date: 2025.06
Description: Tests on 21 top VLMs using the 2600-task PhyBlock benchmark revealed weak high-level physical planning skills, which Chain-of-Thought (CoT) prompting failed to effectively improve.
Link: https://phyblock.github.io/
Domain: Embodied AI VLM VQA

A Generalist Agent

Date: 2022.05
Description: Gato is a multi-modal, multi-task, multi-embodiment generalist agent with 1.2B parameters trained on 604 tasks. Using the same network weights, it can play Atari, caption images, chat, and control real robots.
Domain: Robotics Multi-modal Learning Reinforcement Learning

RT-1: Robotics Transformer for Real-World Control at Scale

Date: 2022.12
Description: RT-1 is a Transformer-based robot control model trained on 130,000+ real-world episodes covering 700+ tasks collected from 13 robots over 17 months, demonstrating strong generalization to new tasks and environments.
Domain: Robotics Multi-task Learning Real-World Control

Pi0: A Vision-Language-Action Flow Model for General Robot Control

Date: 2024.10
Description: π0 is a vision-language-action model built on a 3B parameter pre-trained VLM using flow matching for action generation. Trained on diverse data from 7+ robot platforms across 68+ tasks, enabling dexterous manipulation like laundry folding.
Domain: Robotics Vision-Language-Action Model

OpenVLA: An Open-Source Vision-Language-Action Model

Date: 2024.06
Description: OpenVLA is a 7B-parameter open-source vision-language-action model trained on 970k robot demonstrations that takes language instructions and camera images as input to predict robot actions, supporting cross-embodiment control and efficient fine-tuning for new tasks.
Domain: Embodied AI Robotics Vision-Language

Safety-Critical Kinematic Control of Robotic Systems

Date: 2020.09
Description: A safety-critical control framework that extends control barrier functions (CBFs) to kinematic equations of robotic systems, enabling velocity-based safety guarantees and introducing a new CBF formulation incorporating kinetic energy to minimize model dependence.
Domain: Robotics Control Safety-Critical Control

Diffusion Policy: Visuomotor Policy Learning via Action Diffusion

Date: 2023.03
Description: Diffusion Policy represents robot visuomotor policies as conditional denoising diffusion processes, learning action distribution score functions to generate robot behaviors that handle multimodal actions, high-dimensional spaces, and achieve robust training stability.
Domain: Robotics Imitation Learning Diffusion Models

Open X-Embodiment: Robotic Learning Datasets and RT-X Models

Date: 2023.10
Description: Open X-Embodiment is a large-scale robotics dataset pooling data from 22 different robot embodiments across 21 institutions with 1M+ trajectories, and RT-X models trained on this data demonstrate positive cross-embodiment transfer and improved generalization across multiple robots.
Domain: Robotics Dataset Cross-Embodiment

Do As I Can, Not As I Say: Grounding Language in Robotic Affordances

Date: 2022.04
Description: SayCan grounds large language models in robotic affordances by combining LLM probabilities for task usefulness with value functions for action feasibility, enabling robots to execute long-horizon, abstract natural language instructions in real-world environments.
Domain: Robotics Embodied AI LLM

4.2 Navigation

Matterport3D: Learning from RGB-D Data in Indoor Environments

Date: 2017.09
Description: Matterport3D introduces a comprehensive, large-scale dataset of RGB-D images and 3D reconstructions from 90 different buildings to facilitate the training of algorithms for a variety of scene understanding tasks.
Domain: 3D perception

AI2-THOR: An Interactive 3D Environment for Visual AI

Date: 2017.12
Description: AI2-THOR is an interactive framework of near photo-realistic 3D indoor scenes, designed to train AI agents to navigate and interact with objects.
Domain: Embodied AI Imitation Learning

Interactive Gibson Benchmark (iGibson 0.5): A Benchmark for Interactive Navigation in Cluttered Environments

Date: 2019.10
Description: The Interactive Gibson Benchmark (iGibson) provides a simulation platform with realistic physics for training robotic agents to navigate cluttered environments by physically interacting with objects, like pushing chairs or opening cabinets, to clear a path.
Domain: motion planning interactive navigation

RoboTHOR: An Open Simulation-to-Real Embodied AI Platform

Date: 2020.04
Description: RoboTHOR is an open-source platform that enables the training of AI agents in simulated apartment environments and the direct transfer of those learned skills to a physical robot in a matched real-world setting.
Domain: Embodied AI sim-to-real

HM3D-OVON: A Dataset and Benchmark for Open-Vocabulary Object Goal Navigation

Date: 2024.09
Description: The HM3D-OVON benchmark specifically challenges an AI agent to find an object within a large-scale, photorealistic 3D environment using only a free-form text description (e.g., "find the green cushion on the sofa"), pushing beyond predefined object lists to test true language-grounded navigation.
Domain: Embodied AI VLM

Vision-and-Language Navigation: Interpreting visually-grounded navigation instructions in real environments

Date: 2017.11
Description: This foundational work establishes the Vision-and-Language Navigation (VLN) challenge, requiring an AI agent to navigate through real photographic environments by following step-by-step human language instructions, and introduces the corresponding Room-to-Room (R2R) dataset as a benchmark for this task.
Domain: Embodied AI Robotics

Room-Across-Room: Multilingual Vision-and-Language Navigation with Dense Spatiotemporal Grounding

Date: 2020.10
Description: Room-Across-Room (RxR) introduces a large-scale, multilingual (English, Hindi, and Telugu) dataset for Vision-and-Language Navigation that provides dense spatiotemporal grounding by time-aligning each word of an instruction to the virtual poses of the human annotators.
Domain: Embodied AI VLN

REVERIE: Remote Embodied Visual Referring Expression in Real Indoor Environments

Date: 2019.04
Description: REVERIE proposes a new task and dataset that challenges an embodied AI agent to first navigate to a distant location in a photorealistic indoor scene and then identify a specific object based on a concise natural language description (a referring expression).
Domain: Embodied AI VLN

Touchdown: Natural Language Navigation and Spatial Reasoning in Visual Street Environments

Date: 2018.11
Description: Touchdown introduces a dataset and task where an AI agent must navigate through real-world street view imagery by following natural language instructions that require significant spatial reasoning, such as finding and resolving the location of a hidden object marked in a separate image.
Domain: Embodied AI VLN spatial reasoning

The RobotSlang Benchmark: Dialog-guided Robot Localization and Navigation

Date: 2020.10
Description: The RobotSlang benchmark introduces a new challenge where a lost robot navigates a 3D environment to a target by engaging in a natural language dialogue with a person who is guiding it based on what the robot sees.
Domain: Embodied AI Robotics robot localization

R2H: Building Multimodal Navigation Helpers that Respond to Help Requests

Date: 2023.05
Description: The R2H (Request to Help) framework introduces the task of building an AI navigation helper that not only follows instructions but can also proactively ask for clarification or assistance from a human when it becomes uncertain.
Domain: Embodied AI Human-AI Interaction

Vision-and-Dialog Navigation

Date: 2019.07
Description: Vision-and-Dialog Navigation introduces a task where a navigator agent, who can see but doesn't know the goal, holds a conversation with a question-answering oracle, who knows the goal but can't see, to efficiently navigate a 3D environment.
Domain: Embodied AI interactive and collaborative navigation

UNMuTe: Unifying Navigation and Multimodal Dialogue-like Text Generation

Date: 2024.08
Description: UNMuTe presents a unified framework that trains a single AI agent to simultaneously navigate 3D environments and generate rich, multimodal, dialogue-like text that explains its actions and perceptions along the path.
Domain: Embodied AI VLN NLG

Vision-and-Language Navigation Today and Tomorrow: A Survey in the Era of Foundation Models

Date: 2024.07
Description: This comprehensive survey organizes the field of Vision-and-Language Navigation (VLN), reviewing its historical progress, categorizing current methods, and charting future research directions through the modern lens of large-scale foundation models.
Domain: Embodied AI survey

Research on Navigation Methods Based on LLMs

Date: 2025.04
Description: This survey provides a comprehensive review of navigation methods that leverage Large Language Models (LLMs), categorizing them into different architectures and analyzing how LLMs contribute to planning, reasoning, and understanding instructions.
Domain: Embodied AI survey foundation models

NavCoT: Boosting LLM-Based Vision-and-Language Navigation via Learning Disentangled Reasoning

Date: 2024.03
Description: NavCoT introduces a "Navigational Chain-of-Thought" strategy that trains a Large Language Model to improve its navigation decisions by first imagining the next visual scene based on the instructions, then filtering its view to match that imagination, and finally selecting an action.
Domain: Embodied AI VLN

Object Goal Navigation using Goal-Oriented Semantic Exploration

Date: 2020.07
Description: This work proposes a goal-oriented exploration strategy for object navigation where an AI agent intelligently explores an unknown environment by using its semantic knowledge to prioritize searching in areas most likely to contain the target object (e.g., looking for a 'mug' in the 'kitchen').
Domain: Embodied AI semantic exploration active perception

Object Goal Navigation with Recursive Implicit Maps

Date: 2023.08
Description: This work introduces a method for object goal navigation where the agent builds a 3D map of its environment in real-time using an implicit neural representation, allowing it to efficiently explore and find target objects without needing a pre-built map.
Domain: Embodied AI SLAM

Advancing Object Goal Navigation Through LLM-enhanced Object Affinities Transfer

Date: 2024.03
Description: The LOAT (LLM-enhanced Object Affinities Transfer) framework improves robot navigation by dynamically fusing the broad, commonsense knowledge of a Large Language Model with the robot's own learned experiences to more intelligently predict where a target object is likely to be.
Domain: Embodied AI Object Goal Navigation

LGR: LLM-Guided Ranking of Frontiers for Object Goal Navigation

Date: 2025.03
Description: LGR is an exploration method that improves object navigation by having a Large Language Model rank all possible exploration frontiers based on which direction is most likely to lead to the target object.
Domain: Embodied AI Object Goal Navigation

CL-CoTNav: Closed-Loop Hierarchical Chain-of-Thought for Zero-Shot Object-Goal Navigation with Vision-Language Models

Date: 2025.04
Description: CL-CoTNav introduces a zero-shot navigation method where a Vision-Language Model creates a hierarchical plan using chain-of-thought reasoning, which it then continuously corrects and refines based on real-time visual feedback from the environment.
Domain: Embodied AI VLM zero-shot

Stairway to Success: An Online Floor-Aware Zero-Shot Object-Goal Navigation Framework via LLM-Driven Coarse-to-Fine Exploration

Date: 2025.05
Description: ASCENT introduces a zero-shot, floor-aware navigation framework that enables a robot to find objects in an unknown multi-story building by dynamically creating a 3D map with stair-awareness and using a coarse-to-fine exploration strategy driven by a Large Language Model.
Domain: Embodied AI zero-shot

BabyWalk: Going Farther in Vision-and-Language Navigation by Taking Baby Steps

Date: 2020.05
Description: BabyWalk is a curriculum learning strategy that improves a navigation agent's performance on long, complex routes by first training it on shorter, simpler sub-trajectories before gradually increasing the difficulty.
Domain: Embodied AI VLN

ADAPT: Vision-Language Navigation with Modality-Aligned Action Prompts

Date: 2022.05
Description: ADAPT improves vision-language navigation by using a large language model to generate descriptive "action prompts" for each possible viewpoint, which helps the agent better align its visual observations with the natural language instructions.
Domain: Embodied AI VLN

History Aware Multimodal Transformer for Vision-andLanguage Navigation

Date: 2021.10
Description: The History Aware Multimodal Transformer (HAMT) is a navigation model that uses a transformer architecture to effectively fuse and reason over the agent's full history of visual observations and language instructions, leading to better decision-making.
Domain: Embodied AI VLN

Learning to Navigate Unseen Environments: Back Translation with Environmental Dropout

Date: 2019.04
Description: This work improves a navigation agent's ability to generalize to new environments by generating a vast amount of new training data through back translation (creating instructions for existing paths) and environmental dropout (masking parts of the environment to create variations).
Domain: Embodied AI VLN

Think Global, Act Local: Dual-scale Graph Transformer for Vision-and-Language Navigation

Date: 2022.02
Description: The Dual-scale Graph Transformer is a navigation architecture that simultaneously models the global environment as a coarse graph and local viewpoints as a fine-grained graph, enabling the agent to make locally optimal decisions that are globally consistent.
Domain: Embodied AI VLN

NavGPT: Explicit Reasoning in Vision-and-Language Navigation with Large Language Models

Date: 2023.05
Description: NavGPT is a navigation framework that prompts a Large Language Model to explicitly reason about its progress by breaking down the main instruction into sub-goals, which it then uses to guide a low-level agent through the environment.
Domain: Embodied AI VLN

VELMA: Verbalization Embodiment of LLM Agents for Vision and Language Navigation in Street View

Date: 2023.07
Description: VELMA is a framework that improves vision-and-language navigation in street environments by prompting a Large Language Model to "verbalize" its thought process, generating explicit reasoning steps, environmental descriptions, and self-corrections to guide its actions.
Domain: Embodied AI VLN

NaVILA: Legged Robot Vision-Language-Action Model for Navigation

Date: 2024.12
Description: NaVILA is an open-source vision-language-action model specifically designed for real-world legged robots, enabling them to follow natural language commands to navigate complex indoor and outdoor environments.
Domain: Embodied AI sim-to-real

Vision-Dialog Navigation by Exploring Cross-modal Memory

Date: 2020.03
Description: This work introduces a navigation model with a cross-modal memory component that allows an agent to dynamically store and recall the most relevant information from both its visual history and the ongoing dialogue to make better navigation decisions.
Domain: Embodied AI Vision-and-Dialog Navigation

Goal-oriented Vision-and-Dialog Navigation via Reinforcement Learning

Date: 2022
Description: This work trains a navigation agent using reinforcement learning to actively ask questions and make decisions in order to complete a navigation task, optimizing its policy for both successful navigation and efficient dialogue.
Domain: Embodied AI Vision-and-Dialog Navigation Reinforcement Learning

LLM ContextBridge: A Hybrid Approach for Intent and Dialogue Understanding in IVSR

Date: 2025
Description: LLM ContextBridge proposes a hybrid system that combines the contextual understanding of a Large Language Model with the speed and reliability of a conventional NLU model to improve intent recognition and dialogue understanding in in-vehicle voice systems.
Domain: HCI NLU conversational AI

FLAME: Learning to Navigate with Multimodal LLM in Urban Environments

Date: 2024.08
Description: FLAME introduces a multimodal Large Language Model-based agent that is specifically adapted for urban navigation through a three-phase tuning technique, leveraging automatically synthesized data to significantly improve performance on street-level navigation tasks.
Domain: Embodied AI VLN

Can LLM be a Good Path Planner based on Prompt Engineering? Mitigating the Hallucination for Path Planning

Date: 2024.08
Description: This work introduces a prompt engineering framework called Prompt-and-Exemplar Engineering (PEE) that significantly improves the ability of Large Language Models to solve complex path planning problems by providing them with structured map information and examples.
Domain: Robotics motion planning

Web Agents with World Models: Learning and Leveraging Environment Dynamics in Web Navigation

Date: 2024.10
Description: This work introduces a web navigation agent that learns a "world model" of website dynamics, enabling it to predict the outcomes of its actions and plan its steps more effectively to complete complex tasks.
Domain: autonomous web agents HCI

TWIST: Teacher-Student World Model Distillation for Efficient Sim-to-Real Transfer

Date: 2023.11
Description: TWIST is a framework that improves sim-to-real transfer by distilling a complex, accurate "teacher" world model trained in simulation into a simpler "student" model that can run efficiently on a real robot.
Domain: world model sim-to-real knowledge distillation

4.3 Autonomous Driving

A Survey of Deep Learning Techniques for Autonomous Driving

Date: 2019.10
Description: This survey provides a comprehensive overview of the state-of-the-art deep learning techniques used in autonomous driving, covering everything from perception and path planning to end-to-end learning systems.
Domain: literature review

Human Motion Trajectory Prediction: A Survey

Date: 2019.05
Description: This survey presents a comprehensive overview of deep learning-based methods for predicting human motion trajectories, categorizing them based on their motion modeling and interaction modeling approaches.
Domain: literature review

A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles

Date: 2016.04
Description: This survey provides a structured overview of motion planning and control techniques for self-driving cars in urban settings, categorizing approaches from traditional robotics and control theory to modern data-driven methods.
Domain: literature review motion planning control theory

End to End Learning for Self-Driving Cars

Date: 2016.04
Description: This influential work from NVIDIA demonstrates that a convolutional neural network can learn the entire task of lane-keeping for a self-driving car by directly mapping raw input pixels from a single front-facing camera to steering commands.
Domain: end-to-end

CommonRoad: Composable benchmarks for motion planning on roads

Date: 2017.06
Description: CommonRoad is a suite of composable and open-source benchmarks for motion planning that provides a wide variety of traffic scenarios, enabling researchers to create, compare, and solve complex motion planning problems for autonomous vehicles.
Domain: motion planning benchmark

NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles

Date: 2021.06
Description: nuPlan is a large-scale, closed-loop machine learning benchmark for autonomous vehicle planning that provides real-world driving data and a simulation framework to develop and validate planners in realistic scenarios.
Domain: motion planning benchmark

nuScenes: A multimodal dataset for autonomous driving

Date: 2019.03
Description: nuScenes is a large-scale, multimodal dataset for autonomous driving that features a full 360-degree sensor suite including cameras, LiDAR, and radar, complete with detailed 3D bounding box annotations for 23 object classes.
Domain: object detection tracking

Scalability in Perception for Autonomous Driving: Waymo Open Dataset

Date: 2019.12
Description: The Waymo Open Dataset is a massive and diverse collection of high-resolution sensor data, including LiDAR and cameras, captured across various urban and suburban environments to spur research in perception for autonomous driving.
Domain: object detection tracking

Vision meets robotics: The KITTI dataset

Date: 2013.08
Description: The KITTI dataset is a seminal and challenging real-world benchmark for autonomous driving that provides calibrated and synchronized data from a variety of sensors, including cameras, LiDAR, and GPS/IMU, recorded in diverse urban and rural traffic scenarios.
Domain: object detection stereo vision

The Cityscapes Dataset for Semantic Urban Scene Understanding

Date: 2016.04
Description: The Cityscapes Dataset is a large-scale collection of diverse urban street scenes with high-quality, pixel-level semantic annotations for 30 object classes, designed to benchmark and advance semantic scene understanding.
Domain: semantic segmentation

Argoverse: 3D Tracking and Forecasting with Rich Maps

Date: 2019.11
Description: The Argoverse dataset provides a rich, large-scale collection of 3D tracking and motion forecasting data from a fleet of self-driving cars, complete with detailed, high-resolution maps to support research in autonomous vehicle perception and prediction.
Domain: 3D object tracking motion forecasting

One Thousand and One Hours: Self-driving Motion Prediction Dataset

Date: 2020.06
Description: The "One Thousand and One Hours" dataset is a massive, large-scale collection of real-world driving data with over 1000 hours of sensor logs and 16 million annotated objects, designed for motion prediction and other self-driving tasks.
Domain: behavior prediction motion forecasting

The ApolloScape Open Dataset for Autonomous Driving and its Application

Date: 2018.03
Description: ApolloScape is a massive, open-source dataset for autonomous driving that provides a wealth of real-world and synthetic data with high-quality, per-pixel annotations to support a wide range of tasks from 3D perception to trajectory forecasting.
Domain: semantic scene understanding simulation

BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning

Date: 2018.05
Description: BDD100K is a large and diverse driving dataset that provides 100,000 videos with a rich set of annotations for ten different tasks, aiming to facilitate research in heterogeneous multitask learning for autonomous driving.
Domain: scene understanding

CARLA: An Open Urban Driving Simulator

Date: 2017.11
Description: CARLA is an open-source simulator for autonomous driving research that provides a flexible and realistic urban environment with a wide range of sensor models and controllable environmental conditions.
Domain: simulation

AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles

Date: 2017.05
Description: AirSim is an open-source, high-fidelity simulator for autonomous vehicles built on Unreal Engine, providing physically and visually realistic environments for developing and testing AI for drones and cars.
Domain: simulation sim-to-real

ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst

Date: 2018.12
Description: ChauffeurNet is a machine learning model that learns to drive by imitating a human driver's trajectory, while also being trained on a synthesized dataset of simulated collisions and off-road events to learn how to recover from mistakes.
Domain: imitation learning motion planning

Deep Reinforcement Learning for Autonomous Driving: A Survey

Date: 2020.02
Description: This survey provides a comprehensive review of deep reinforcement learning applications in autonomous driving, categorizing methods and discussing their use in solving complex decision-making problems like path planning and behavior arbitration.
Domain: literature review deep reinforcement learning

Learning Lane Graph Representations for Motion Forecasting

Date: 2020.07
Description: This work, introducing LaneGCN, models the complex topological relationships of road lanes as a graph, allowing an autonomous vehicle to better predict the future trajectories of multiple surrounding agents.
Domain: motion forecasting

Wayformer: Motion Forecasting via Simple & Efficient Attention Networks

Date: 2022.07
Description: The Wayformer is a family of efficient, attention-based models for motion forecasting that effectively captures the complex interactions between agents and the road map to predict future trajectories.
Domain: motion forecasting

DriveDreamer: Towards Real-world-driven World Models for Autonomous Driving

Date: 2023.09
Description: DriveDreamer is a world model for autonomous driving that can generate realistic, controllable, and infinitely long driving scenarios in a closed loop by learning the dynamics of traffic from real-world data.
Domain: Generative AI world model video generation

DriveDreamer4D: World Models Are Effective Data Machines for 4D Driving Scene Representation

Date: 2024.10
Description: DriveDreamer4D is a world model that acts as a "data machine," generating consistent and high-quality 4D data (3D scenes over time) to significantly enhance the performance of various autonomous driving perception tasks.
Domain: Generative AI world model 4D perception

ReconDreamer: Crafting World Models for Driving Scene Reconstruction via Online Restoration

Date: 2024.11
Description: ReconDreamer is a world model that learns to reconstruct and understand 3D driving scenes by being trained to restore intentionally degraded or masked sensor data in an online fashion.
Domain: Generative AI world model scene reconstruction

DrivingDiffusion: Layout-Guided multi-view driving scene video generation with latent diffusion model

Date: 2023.10
Description: DrivingDiffusion is a latent diffusion model that generates realistic, multi-view driving scene videos by using a bird's-eye-view (BEV) layout as a guide to control the scene's structure and dynamics.
Domain: Generative AI video generation diffusion model

BEVControl: Accurately Controlling Street-view Elements with Multi-perspective Consistency via BEV Sketch Layout

Date: 2023.08
Description: BEVControl is a method for generating and editing street-view images by allowing a user to draw a simple bird's-eye-view (BEV) sketch, which then controls the placement and appearance of elements like roads and vehicles with multi-perspective consistency.
Domain: Generative AI scene generation

Vista: A Generalizable Driving World Model with High Fidelity and Versatile Controllability

Date: 2024.05
Description: Vista is a generalizable driving world model that can predict high-fidelity, long-horizon driving scenarios and can be controlled by a versatile set of actions, from high-level commands to low-level vehicle maneuvers.
Domain: Generative AI video prediction world model

HoloDrive: Holistic 2D-3D Multi-Modal Street Scene Generation for Autonomous Driving

Date: 2024.12
Description: HoloDrive is a generative model that creates holistic and consistent street scenes by simultaneously producing multi-camera 2D videos and their corresponding 3D LiDAR point clouds and bird's-eye-view maps.
Domain: Generative AI world model

DrivingWorld: Constructing World Model for Autonomous Driving via Video GPT

Date: 2024.12
Description: DrivingWorld is a world model for autonomous driving that uses a Video Generative Pre-trained Transformer (Video GPT) to learn the dynamics of traffic scenes and generate realistic future driving scenarios.
Domain: Generative AI video prediction world model

DrivingGPT: Unifying Driving World Modeling and Planning with Multi-modal Autoregressive Transformers

Date: 2024.12
Description: DrivingGPT is a multi-modal autoregressive transformer model that unifies world modeling and planning, allowing it to both predict the future evolution of a driving scene and make driving decisions within a single, end-to-end framework.
Domain: end-to-end world model

OccWorld: Learning a 3D Occupancy World Model for Autonomous Driving

Date: 2023.11
Description: OccWorld is a world model that learns to predict the future evolution of a 3D driving scene by representing the world as a 3D occupancy grid and using a generative transformer to forecast both the movement of the ego-vehicle and the surrounding environment.
Domain: Generative AI 3D prediction world model

OccLLaMA: An Occupancy-Language-Action Generative World Model for Autonomous Driving

Date: 2024.09
Description: OccLLaMA is a generative world model that unifies 3D occupancy prediction, language-based reasoning, and action generation into a single framework, allowing it to understand, explain, and plan in complex driving scenarios.
Domain: end-to-end world model

RenderWorld: World Model with Self-Supervised 3D Label

Date: 2024.09
Description: RenderWorld is a world model for autonomous driving that learns to predict future 3D scenes by generating its own self-supervised 3D labels, eliminating the need for expensive manual annotation.
Domain: 3D prediction world model

Driving in the Occupancy World: Vision-Centric 4D Occupancy Forecasting and Planning via World Models for Autonomous Driving

Date: 2024.08
Description: This work introduces a vision-centric world model that forecasts the future 4D occupancy (3D space + time) of a driving scene and uses this prediction to directly plan the vehicle's trajectory.
Domain: 4D occupancy forecasting end-to-end world model

DOME: Taming Diffusion Model into High-Fidelity Controllable Occupancy World Model

Date: 2024.10
Description: DOME is a framework that adapts a diffusion model to create a high-fidelity and controllable world model, which can generate realistic future 3D occupancy grids for driving scenes based on specified actions.
Domain: 3D scene forecasting diffusion model world model

Copilot4D: Learning Unsupervised World Models for Autonomous Driving via Discrete Diffusion

Date: 2023.11
Description: Copilot4D is an unsupervised world model that learns to predict the future 4D (3D space + time) evolution of a driving scene by using a discrete diffusion process on compressed 3D representations.
Domain: 4D perception diffusion model world model Generative AI

UltraLiDAR: Learning Compact Representations for LiDAR Completion and Generation

Date: 2023.11
Description: UltraLiDAR introduces a method that learns a compact and efficient representation of LiDAR data, enabling both the completion of sparse, real-world LiDAR scans and the generation of entirely new, realistic point clouds.
Domain: point cloud completion generative model

HERMES: A Unified Self-Driving World Model for Simultaneous 3D Scene Understanding and Generation

Date: 2025.01
Description: HERMES is a unified world model for autonomous driving that can simultaneously perform 3D scene understanding (like perception and tracking) and generate realistic future driving scenarios within a single framework.
Domain: 3D perception scene generation world model Generative AI

DreamDrive: Generative 4D Scene Modeling from Street View Images

Date: 2025.01
Description: DreamDrive is a generative framework that synthesizes controllable and realistic 4D (3D space + time) driving scenes by combining the generative power of video diffusion models with the 3D consistency of Gaussian splatting.
Domain: 4D scene generation neural rendering

Stag-1: Towards Realistic 4D Driving Simulation with Video Generation Model

Date: 2024.12
Description: Stag-1 is a video generation model designed to create realistic and controllable 4D driving simulations by using a cascaded architecture that first generates a global scene layout and then adds fine-grained details.
Domain: video generation world model Generative AI

Occ3D: A Large-Scale 3D Occupancy Prediction Benchmark for Autonomous Driving

Date: 2023.04
Description: Occ3D is a large-scale benchmark and dataset specifically designed for the task of 3D occupancy prediction, providing standardized metrics and a robust framework for evaluating and comparing different models.
Domain: 3D perception scene understanding benchmark

Argoverse 2: Next Generation Datasets for Self-Driving Perception and Forecasting

Date: 2023.01
Description: Argoverse 2 is a collection of four large-scale, open-source datasets for autonomous driving that provide high-resolution sensor data, 3D maps, and millions of annotated scenarios to advance research in perception and motion forecasting.
Domain: 3D perception motion forecasting sensor fusion

Bench2Drive: Towards Multi-Ability Benchmarking of Closed-Loop End-To-End Autonomous Driving

Date: 2024.06
Description: Bench2Drive is a comprehensive, closed-loop benchmark for end-to-end autonomous driving systems that provides a large, standardized training dataset and a multi-ability evaluation protocol to fairly assess and compare different driving models in a variety of interactive scenarios.
Domain: end-to-end learning benchmark

S2R-Bench: A Sim-to-Real Evaluation Benchmark for Autonomous Driving

Date: 2025.05
Description: S2R-Bench is a sim-to-real benchmark that provides a collection of real-world sensor data with anomalies (like snow and fog) to evaluate and improve the robustness of autonomous driving perception algorithms.
Domain: sim-to-real benchmark

Interaction-Aware Trajectory Planning for Autonomous Vehicles with Analytic Integration of Neural Networks into Model Predictive Control

Date: 2023.01
Description: This work presents an interaction-aware trajectory planning method that analytically integrates a neural network, which predicts the behavior of other vehicles, directly into a model predictive control framework for more efficient and socially-aware navigation.
Domain: motion planning MPC

DriveCoT: Integrating Chain-of-Thought Reasoning with End-to-End Driving

Date: 2024.03
Description: DriveCoT is an end-to-end driving framework that integrates chain-of-thought reasoning by generating explicit textual justifications for its driving decisions, improving the model's interpretability and performance.
Domain: end-to-end

PRIMEDrive-CoT: A Precognitive Chain-of-Thought Framework for Uncertainty-Aware Object Interaction in Driving Scene Scenario

Date: 2025.04
Description: PRIMEDrive-CoT is a framework that improves a driving model's ability to handle uncertain interactions with other objects by using a "precognitive" chain-of-thought process to anticipate multiple possible future outcomes before making a decision.
Domain: motion forecasting interpretable AI

LeapVAD: A Leap in Autonomous Driving via Cognitive Perception and Dual-Process Thinking

Date: 2025.01
Description: LeapVAD is a novel autonomous driving framework that enhances decision-making by combining cognitive perception with a dual-process learning system, which allows it to achieve superior performance with limited training data by mimicking human-like attention and reasoning.
Domain: cognitive AI knowledge-driven system

DriveLMM-o1: A Step-by-Step Reasoning Dataset and Large Multimodal Model for Driving Scenario Understanding

Date: 2025.03
Description: DriveLMM-o1 introduces a large-scale dataset and a corresponding multimodal model designed to advance step-by-step visual reasoning in autonomous driving by providing detailed annotations for perception, prediction, and planning.
Domain: interpretable AI VQA

Reason2Drive: Towards Interpretable and Chain-based Reasoning for Autonomous Driving

Date: 2023.12
Description: Reason2Drive is a framework that improves the interpretability of autonomous driving systems by training a model to generate explicit, chain-like textual reasoning for its high-level decisions.
Domain: interpretable AI XAI

TeraSim-World: Worldwide Safety-Critical Data Synthesis for End-to-End Autonomous Driving

Date: 2025.09
Description: TeraSim-World is a data synthesis system that can generate massive, worldwide, safety-critical driving scenarios to train and test end-to-end autonomous driving models in rare but dangerous situations.
Domain: data synthesis end-to-end learning

Cosmos-Drive-Dreams: Scalable Synthetic Driving Data Generation with World Foundation Models

Date: 2025.06
Description: Cosmos-Drive-Dreams is a framework that uses world foundation models to generate large-scale, diverse, and high-fidelity synthetic driving data for training and testing autonomous driving systems.
Domain: data synthesis world model

RoboTron-Sim: Improving Real-World Driving via Simulated Hard-Case

Date: 2025.08
Description: RoboTron-Sim is a simulation platform designed to improve the real-world performance of driving models by specifically training them on a large and diverse set of simulated, safety-critical "hard cases".
Domain: safety validation sim-to-real

Think2Drive: Efficient Reinforcement Learning by Thinking in Latent World Model for Quasi-Realistic Autonomous Driving (in CARLA-v2)

Date: 2024.02
Description: Think2Drive is a reinforcement learning framework that improves the sample efficiency of autonomous driving agents by training them to "think" and plan within a learned, compressed latent world model of the CARLA-v2 simulator.
Domain: model-based RL world model

A Survey on Safety-Critical Driving Scenario Generation – A Methodological Perspective

Date: 2022.02
Description: This survey provides a comprehensive methodological review of algorithms for generating safety-critical driving scenarios, categorizing them into data-driven, adversarial, and knowledge-based approaches.
Domain: literature review scenario generation

C. Physics Reasoning AI

C.2 Symbolic Reasoning Frameworks

Physics-AI symbiosis

Date: 2022.09
Description: Proposes the concept of "Physics-AI Symbiosis," a comprehensive review of the bidirectional and mutually beneficial relationship between physics and artificial intelligence.
Domain: AI for Physics Physics for AI Review Interdisciplinary Scientific Discovery

AI meets physics: a comprehensive survey

Date: 2024.08
Description: A comprehensive survey on the bidirectional relationship between AI and physics, detailing how physics principles inspire AI models (Physics for AI) and how AI empowers physical science research (AI for Physics).
Domain: AI for Physics Physics for AI Review Interdisciplinary Machine Learning Theory

C.2.1 Equation-based Reasoning Systems (equation discovery, symbolic regression)

Toward an AI Physicist for Unsupervised Learning

Date: 2019.09
Description: Proposes a new paradigm for unsupervised learning centered on an 'AI Physicist' agent that discovers, simplifies, and organizes 'theories' (prediction function + domain of applicability) from observational data. Key innovations include a generalized-mean loss for unsupervised domain specialization (divide-and-conquer), a differentiable Minimum Description Length (MDL) objective for simplification (Occam's Razor), and a 'theory hub' for unification and lifelong learning. This work serves as the conceptual precursor to the AI Feynman algorithm.
Domain: AI for Science Unsupervised Learning Equation Discovery Occam's Razor Divide and Conquer

Intelligence, physics and information – the tradeoff between accuracy and simplicity in machine learning

Date: 2020.01
Description: A foundational thesis that frames machine learning through the lens of physics and information theory, proposing the information bottleneck principle as a universal framework for navigating the accuracy-simplicity tradeoff inherent in scientific discovery.
Domain: Information Theory Machine Learning Theory Scientific Discovery Symbolic Regression Interpretable AI

Discovering physical concepts with neural networks

Date: 2020.01
Description: Introduces a science-agnostic neural network that discovers fundamental physical concepts, like conserved quantities, from raw observational data in an unsupervised manner by using an information bottleneck.
Domain: Scientific Discovery Unsupervised Learning Interpretable AI Conceptual Physics Information Bottleneck

AI Feynman: A physics-inspired method for symbolic regression

Date: 2020.04
Description: Introduces a novel, physics-inspired algorithm for symbolic regression that recursively discovers symbolic expressions from data. The method uses a neural network to approximate the unknown function and then applies a suite of physics-inspired techniques (e.g., dimensional analysis, symmetry detection, separability) to recursively break the problem down into simpler ones, which are finally solved by a brute-force search. It successfully rediscovered 100 equations from the Feynman Lectures on Physics.
Domain: Symbolic Regression AI for Science Equation Discovery Neural Networks Physics-Inspired AI

AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity

Date: 2020.06
Description: An improved version of the AI Feynman algorithm introducing three key innovations: (1) seeking a Pareto-optimal frontier of formulas that balance accuracy and complexity, (2) using neural network gradients to discover generalized symmetries and arbitrary graph modularity, and (3) employing Normalizing Flows to extend symbolic regression to probability distributions. The method demonstrates significantly enhanced robustness to noise and solves more complex problems than its predecessor.
Domain: Symbolic Regression AI for Science Pareto Optimality Normalizing Flows Equation Discovery

AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledge

Date: 2025.04
Description: AI-Newton, a concept-driven discovery system, can autonomously derive physical laws from raw data—without supervision or prior physical knowledge. The system integrates a knowledge base and knowledge representation centered around physical concepts, as well as an autonomous discovery workflow.
Domain: Survey Symbolic-AI

Bayesian symbolic regression: Automated equation discovery from a physicists' perspective

Date: 2025.07
Description: Discusses a probabilistic approach to symbolic regression rooted in Bayesian inference, arguing for model plausibility and ensembles over heuristic criteria to provide a more rigorous framework for automated equation discovery.
Domain: Symbolic Regression Bayesian Inference Automated Scientific Discovery Model Selection Review

C.2.2 Neuro-Symbolic Integration, Differentiable Physics Engines

KAN: Kolmogorov-Arnold Networks

Date: 2024.04
Description: Inspired by the Kolmogorov-Arnold representation theorem, this paper introduces Kolmogorov-Arnold Networks (KANs) as a powerful and interpretable alternative to Multi-Layer Perceptrons (MLPs). KANs feature learnable activation functions on the edges (parameterized as splines) instead of fixed activations on the nodes. This fundamental architectural shift results in superior accuracy and better scaling laws on various tasks, including function fitting and PDE solving. Most importantly, their structure is inherently interpretable, making them a promising tool for scientific discovery.
Domain: Neural Network Architecture Kolmogorov-Arnold Theorem Interpretability Symbolic Regression AI for Science

KAN 2.0: Kolmogorov-Arnold Networks Meet Science

Date: 2024.08
Description: This work elevates KANs from a neural network architecture to a comprehensive, bidirectional framework for scientific discovery. It establishes a synergy between science and KANs, enabling both the incorporation of scientific knowledge into KANs (via auxiliary variables, modular structures, and a novel "kanpiler" for compiling formulas) and the extraction of scientific insights from them (via feature attribution, a "tree converter" for modularity, and symbolic simplification). The paper also introduces MultKAN, an extension that includes native multiplication nodes, enhancing interpretability and efficiency.
Domain: KAN AI for Science Interpretability Scientific Discovery Symbolic Regression

C.3 Physics-Informed Neural Networks

C.3.1 Macro Perspectives on Physics-Informed Machine Learning (PIML)

Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data

Date: 2017.06
Description: A foundational paper that conceptualizes Theory-Guided Data Science (TGDS), proposing a taxonomy of five themes for integrating scientific knowledge with data science models to improve generalization and interpretability.
Domain: Conceptual Framework Theory-Guided Data Science Scientific Discovery Review PIML

Physics-informed machine learning

Date: 2021.06
Description: A comprehensive review that frames Physics-Informed Machine Learning (PIML) as a new paradigm for integrating data and physical models. It categorizes the methods for embedding physics into machine learning into three types of biases: observational, inductive (architectural), and learning (loss function). The paper surveys the capabilities, limitations, and diverse applications of PIML, positioning PINNs as a key component within this broader field.
Domain: Physics-Informed Machine Learning Review PINN Inductive Bias Scientific Machine Learning

Hybrid physics-based and data-driven models for smart manufacturing: Modelling, simulation, and explainability

Date: 2022.04
Description: This review paper provides a systematic overview of hybrid physics-based and data-driven models specifically for smart manufacturing applications. It categorizes these hybrid models into three main types: (1) physics-informed machine learning (e.g., PINNs), where physical laws constrain the learning process; (2) machine learning-assisted simulation (e.g., surrogate modeling), where ML accelerates or enhances traditional physics-based simulations; and (3) explainable AI (XAI), which aims to interpret the behavior of complex models. The paper highlights the complementary strengths of physics and data, offering a practical framework for developing more transparent, interpretable, and accurate models in industrial settings.
Domain: Review Hybrid Modeling Physics-Informed Machine Learning Explainable AI Smart Manufacturing

Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications

Date: 2022.11
Description: A comprehensive survey that systematically reviews the field of Physics-Informed Machine Learning (PIML) from a machine learning perspective, proposing a taxonomy based on tasks, types of physical priors, and methods of incorporation.
Domain: Survey PIML Physics-Informed Machine Learning Taxonomy Review

Physics-Informed Neural Networks: A Review of Methodological Evolution, Theoretical Foundations, and Interdisciplinary Frontiers Toward Next-Generation Scientific Computing

Date: 2025.07
Description: A comprehensive and up-to-date review of the Physics-Informed Neural Network (PINN) landscape. The paper systematically categorizes the field's progress into three main axes: methodological evolution (innovations in loss functions, architectures, and training strategies), theoretical foundations (error analysis and connections to classical methods), and interdisciplinary frontiers (applications beyond traditional physics). It provides a structured roadmap for understanding the state-of-the-art and future directions of PINNs as a next-generation scientific computing tool.
Domain: Review PINN Scientific Machine Learning Physics-Informed AI Computational Science

Training of physical neural networks

Date: 2025.09
Description: A comprehensive review of training methodologies for Physical Neural Networks (PNNs), which use analogue physical systems for computation, categorizing them into in-situ and ex-situ backpropagation strategies and outlining the field's future potential.
Domain: Physical Neural Networks Analogue Computing Physics-Aware Training Review

C.3.2 PINNs for Scalability: Addressing Large-Scale and Complex Problems

General Frameworks & Foundations:

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Date: 2017.11
Description: This is the first part of the original two-part treatise that introduced Physics-Informed Neural Networks. It specifically focuses on the forward problem: using PINNs as data-efficient function approximators to infer the solutions of PDEs. The framework embeds physical laws as soft constraints in the neural network's loss function, demonstrating how to obtain accurate solutions from sparse boundary and initial condition data. It introduces both continuous-time and discrete-time (with Runge-Kutta schemes) models.
Domain: PINN Deep Learning Partial Differential Equations Forward Problems Data-driven Scientific Computing

Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

Date: 2017.11
Description: This work establishes the use of Physics-Informed Neural Networks (PINNs) for solving inverse problems, specifically the data-driven discovery of parameters in nonlinear PDEs. By treating the unknown PDE parameters as trainable variables alongside the neural network's weights, the framework can accurately identify these parameters from sparse and noisy data. It presents a unified approach that handles both forward and inverse problems, demonstrating its power on various physical systems like fluid dynamics, and introduces continuous and discrete time models for different data scenarios.
Domain: PINN Inverse Problems Parameter Identification Equation Discovery Data-driven Scientific Computing

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Date: 2018.11
Description: A seminal framework that introduces Physics-Informed Neural Networks (PINNs), which embed physical laws described by general nonlinear PDEs directly into the neural network's loss function. This acts as a regularization agent, enabling the solution of both forward (data-driven solution) and inverse (data-driven discovery) problems from sparse and noisy data.
Domain: PINN Deep Learning Partial Differential Equations Inverse Problems Data-driven Scientific Computing

Domain Decomposition & Parallelism:

PPINN: Parareal physics-informed neural network for time-dependent PDEs

Date: 2020.07
Description: This paper introduces the Parareal Physics-Informed Neural Network (PPINN), a framework designed to accelerate the solution of long-time integration problems for time-dependent PDEs. It combines the classical Parareal parallel-in-time algorithm with PINNs. The method uses a computationally cheap "coarse" solver to provide a global approximation, while multiple "fine" PINN solvers work in parallel to correct the solution on short time sub-intervals. This hybrid, iterative approach significantly reduces the wall-clock time for long-time simulations by decomposing a serial problem into parallelizable sub-problems.
Domain: PINN PINN Acceleration Parallel Computing Parareal Algorithm Time-dependent PDEs

Finite Basis Physics-Informed Neural Networks (FBPINNs): A scalable domain decomposition approach for solving differential equations

Date: 2021.07
Description: This paper proposes Finite Basis PINNs (FBPINNs), a scalable domain decomposition framework for solving large-scale and multiscale PDEs. The method decomposes the domain and assigns an independent PINN to each subdomain. Critically, it constructs a smooth global solution by treating the local PINN solutions as basis functions and stitching them together using a partition of unity weighting. This approach, inspired by finite element methods, significantly improves the scalability and efficiency of PINNs for challenging problems where standard PINNs fail.
Domain: PINN Domain Decomposition Scalability PINN Acceleration Finite Element Method

When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

Date: 2021.09
Description: This paper provides the first theoretical generalization analysis for Extended Physics-Informed Neural Networks (XPINNs). By deriving and comparing the generalization error bounds for both standard PINNs and XPINNs, the work reveals a fundamental trade-off in domain decomposition: while decomposing a complex function into simpler ones on subdomains reduces the necessary model complexity (improving generalization), the need to enforce interface conditions introduces an additional learning cost that can harm generalization. The authors conclude that XPINNs outperform PINNs if and only if the gain from the reduced function complexity outweighs the cost of learning the interface constraints.
Domain: PINN Domain Decomposition Generalization Theory Machine Learning Theory Scientific Machine Learning

Parallel Physics-Informed Neural Networks via Domain Decomposition

Date: 2021.10
Description: This paper introduces a distributed and parallel framework for PINNs based on the classical domain decomposition method (DDM). The core idea is to break a large computational domain into smaller subdomains, assign an independent, smaller PINN to each subdomain, and enforce physical conservation laws at the interfaces. This approach, implemented for both spatial (cPINN) and spatio-temporal (XPINN) decompositions, enables massive parallelization, significantly accelerating the training process for large-scale problems and offering greater flexibility for multi-physics and multi-scale systems.
Domain: PINN Parallel Computing Domain Decomposition High-Performance Computing PINN Acceleration

Improved Deep Neural Networks with Domain Decomposition in Solving Partial Differential Equations

Date: 2022.09
Description: This paper proposes an improved domain decomposition method for PINNs to tackle large-scale and complex problems. The approach decomposes the computational domain into subdomains, assigning an individual neural network to each. A key insight of the work is framing domain decomposition as a strategy to mitigate the "gradient pathology" issue prevalent in large, single-network PINNs. The method demonstrates superior performance over classical PINNs in terms of training effectiveness, accuracy, and computational cost.
Domain: PINN Domain Decomposition PINN Acceleration Gradient Pathology Scalability

Complex Geometries & Architectures:

Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries

Date: 2022.07
Description: This paper introduces Physics-Informed PointNet (PI-PointNet), a novel deep learning framework that equips PINNs with the ability to handle irregular and varied geometries. It replaces the standard MLP backbone with a PointNet encoder, which learns a global feature representation of the domain's shape from a point cloud of its boundary. This geometry-aware feature is then concatenated with spatial coordinates and fed into an MLP decoder to predict the physical field. This "encode-decode" architecture allows the model to be trained on a collection of different geometries and then generalize to solve PDEs on new, unseen shapes without retraining.
Domain: PINN Architecture PointNet Geometric Deep Learning Irregular Domains AI for Engineering

INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems

Date: 2022.12
Description: This paper proposes Interfaced Neural Networks (INNs) to solve PDE problems with discontinuous coefficients and irregular interfaces, where standard PINNs typically fail. The core idea is a physics-driven domain decomposition: the domain is split along the known interfaces, and a separate neural network is assigned to each subdomain. Crucially, the physical interface conditions (e.g., continuity of the solution and jumps in the flux) are explicitly enforced as loss terms, enabling the framework to accurately capture discontinuities in the solution's derivatives.
Domain: PINN Interface Problems Domain Decomposition Discontinuous Solutions Scientific Machine Learning

Deep neural network methods for solving forward and inverse problems of time fractional diffusion equations with conformable derivative

Date: 2021.08
Description: This paper pioneers the application of Physics-Informed Neural Networks (PINNs) to solve time-fractional diffusion equations involving the conformable derivative, a newer definition in fractional calculus. The work demonstrates that the PINN framework can effectively handle both forward (solution) and inverse (parameter estimation) problems for this class of non-standard PDEs. To address accuracy degradation when the fractional order approaches integer values, the authors introduce a weighted PINN (wPINN) that adjusts the loss function to mitigate the effects of singularities, thereby enhancing the model's robustness.
Domain: PINN Fractional Calculus Conformable Derivative Inverse Problems Scientific Machine Learning

Neural homogenization and the physics-informed neural network for the multiscale problems

Date: 2021.08
Description: This paper introduces Neural Homogenization-PINN (NH-PINN), a method that combines classical homogenization theory with PINNs to solve complex multiscale PDEs. Instead of tackling the challenging multiscale problem directly, NH-PINN employs a three-step process: (1) using PINNs with a proposed oversampling strategy to accurately solve the periodic cell problems at the microscale, (2) computing the effective homogenized coefficients, and (3) using another PINN to solve the much simpler macroscopic homogenized equation. This theoretically-grounded approach significantly improves the accuracy of PINNs for multiscale problems where standard PINNs typically fail.
Domain: PINN Multiscale Modeling Homogenization Theory Scientific Machine Learning Hybrid Modeling

A High-Efficient Hybrid Physics-Informed Neural Networks Based on Convolutional Neural Network

Date: 2021.04
Description: Proposes a hybrid PINN that replaces automatic differentiation with a discrete differential operator learned via a "local fitting method," providing the first theoretical convergence rate for a machine learning-based PDE solver.
Domain: PINN Hybrid Method Numerical Stencil CNN Convergence Rate

A hybrid physics-informed neural network for nonlinear partial differential equation

Date: 2021.12
Description: Proposes a hybrid PINN (hPINN) that uses a discontinuity indicator to switch between automatic differentiation for smooth regions and a classical WENO scheme to capture discontinuities, improving performance on PDEs with shock solutions.
Domain: PINN Hybrid Method WENO Discontinuous Solutions Burgers Equation

Separable Physics-Informed Neural Networks

Date: 2023.12
Description: Proposes Separable Physics-Informed Neural Networks (SPINN) to address the spectral bias issue in solving multiscale PDEs. The core idea is to decompose the solution into multiple components with different characteristic scales (e.g., low- and high-frequency) and use separate, specialized neural network streams for each component. These streams are trained jointly, allowing the model to efficiently and accurately learn complex solutions that standard PINNs fail to capture.
Domain: PINN Architecture Spectral Bias Multiscale Modeling Physics-Informed Machine Learning Fourier Features

LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks

Date: 2025.08
Description: LNN-PINN, a physics-informed neural network framework, combines a liquid residual gating architecture while retaining the original physical modeling and optimization process to improve prediction accuracy.
Domain: PINN Liquid Neural Network

Specialized Applications:

ModalPINN: An extension of physics-informed Neural Networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors

Date: 2022.05
Description: This paper introduces ModalPINN, a specialized PINN architecture designed for reconstructing periodic flows from sparse and noisy sensor data. Instead of learning the high-dimensional spatio-temporal field directly, ModalPINN enforces a strong inductive bias by assuming the solution can be represented by a truncated Fourier series. The neural network's task is reduced to learning the low-dimensional time-dependent coefficients of these Fourier modes. This modal decomposition significantly improves the model's robustness and accuracy in data-limited regimes, outperforming standard PINNs for periodic problems.
Domain: PINN Architecture Flow Reconstruction Fourier Analysis Inductive Bias Scientific Machine Learning

Novel Physics-Informed Artificial Neural Network Architectures for System and Input Identification of Structural Dynamics PDEs

Date: 2023.02
Description: Proposes novel parallel and sequential PINN architectures to solve output-only system and input identification problems in structural dynamics. The method first discretizes the governing PDE into a set of modal ODEs using the Eigenfunction Expansion Method, then assigns individual, cooperating PINNs to each mode, significantly improving computational efficiency, flexibility, and accuracy for complex engineering inverse problems.
Domain: PINN Architecture Structural Dynamics System Identification Inverse Problems Hybrid Model

Physics-informed Neural Motion Planning on Constraint Manifolds

Date: 2024.03
Description: This work introduces a novel physics-informed framework for constrained motion planning (CMP) in robotics. It reformulates the CMP problem as solving the Eikonal PDE on the constraint manifold, which is then solved using a Physics-Informed Neural Network (PINN). This approach is entirely data-free, requiring no expert demonstrations, and learns a neural function that can generate optimal, collision-free paths in sub-seconds. The method significantly outperforms state-of-the-art CMP techniques in speed and success rate on complex, high-dimensional tasks.
Domain: Physics-Informed Neural Networks Robotics Motion Planning Eikonal Equation AI for Engineering

C.3.3 PINNs for Robustness: Accelerating and Stabilizing Training

Multi-Objective Loss Optimization：

A Dual-Dimer method for training physics-constrained neural networks with minimax architecture

Date: 2021.01
Description: Proposes a novel minimax architecture (PCNN-MM) that formulates PINN training as a saddle-point problem to systematically adjust loss weights, and introduces an efficient "Dual-Dimer" algorithm to solve it.
Domain: PINN Loss Balancing Minimax Optimization Saddle Point Search Training Optimization

On Theory-training Neural Networks to Infer the Solution of Highly Coupled Differential Equations

Date: 2021.02
Description: Proposes a Partial Regularization Technique (PRT) to eliminate training oscillations and provides systematic guidelines for finding optimal network architectures, significantly improving the accuracy and robustness of PINNs for highly coupled systems.
Domain: PINN Training Strategy Robustness Network Architecture Regularization

Self-adaptive loss balanced Physics-informed neural networks for the incompressible Navier-Stokes equations

Date: 2021.04
Description: Proposes a self-adaptive method (lbPINNs) that automatically balances multiple loss components in PINNs by modeling each term's contribution through a learnable uncertainty parameter, significantly improving accuracy for complex fluid dynamics.
Domain: PINN Loss Balancing Uncertainty Navier-Stokes Training Optimization

Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations

Date: 2021.05
Description: Proposes enhancing PINNs by combining multi-task learning (jointly training on a related auxiliary PDE) and adversarial training (generating high-loss samples) to improve generalization and accuracy in highly non-linear domains.
Domain: PINN Multi-task Learning Adversarial Training Generalization

Multi-Objective Loss Balancing for Physics-Informed Deep Learning

Date: 2021.10
Description: Proposes a novel self-adaptive algorithm, ReLoBRaLo, which dynamically balances multiple loss terms in PINNs based on their relative progress, an exponential moving average, and a unique random lookback mechanism to improve training speed and accuracy.
Domain: PINN Loss Balancing Multi-Objective Optimization Training Optimization

Adaptive Input and Gradient Strategies：

Learning in Sinusoidal Spaces with Physics-Informed Neural Networks

Date: 2021.09
Description: This paper diagnoses a key failure mode in training PINNs, showing that expressive networks are initialized with a bias towards flat, near-zero functions, trapping them in trivial local minima of the PDE residual loss. To overcome this, it proposes sf-PINN, an architecture that preprocesses inputs with a sinusoidal feature mapping. The authors theoretically prove that this mapping increases input gradient variability at initialization, providing effective gradients for the optimizer to escape these deceptive local minima. This simple, non-intrusive modification is shown to significantly improve the training stability and final accuracy of PINNs.
Domain: PINN Training Pathology Spectral Bias Initialization Input Representation

Robust Learning of Physics Informed Neural Networks

Date: 2021.10
Description: Proposes a robust training framework where a Gaussian Process (GP) is first used to smooth/denoise noisy training data, and the resulting clean "proxy" data is then used to train the PINN, effectively decoupling data denoising from PDE solving.
Domain: PINN Robustness Noisy Data Gaussian Process Data Pre-processing

Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

Date: 2021.11
Description: Proposes Gradient-enhanced PINNs (gPINNs), a method that improves the accuracy and efficiency of PINNs by adding the gradient of the PDE residual as an additional term in the loss function.
Domain: PINN Gradient-enhanced Loss Function Training Optimization RAR

Accelerated Training of Physics-Informed Neural Networks (PINNS) using Meshless Discretizations

Date: 2022.05
Description: Proposes Discretely-Trained PINNs (DT-PINNs), which accelerate training by replacing expensive automatic differentiation for spatial derivatives with a pre-computed, high-order accurate meshless RBF-FD operator, achieving 2-4x speedups.
Domain: PINN Training Acceleration RBF-FD Meshless Method Numerical Differentiation

RPINNS: Rectified-physics informed neural networks for solving stationary partial differential equations

Date: 2022.06
Description: Proposes a Rectified-PINN (RPINN) which, inspired by multigrid methods, uses a second neural network to learn and correct the error of an initial PINN solution, leading to higher final accuracy.
Domain: PINN Iterative Refinement Multigrid High Precision

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Date: 2022.07
Description: Presents a comprehensive benchmark of 10 sampling methods for PINNs and proposes two new residual-based adaptive sampling algorithms (RAD and RAR-D) that significantly improve accuracy by dynamically redistributing points based on the PDE residual.
Domain: PINN Adaptive Sampling RAR Training Optimization Benchmark

A Novel Adaptive Causal Sampling Method for Physics-Informed Neural Networks

Date: 2022.10
Description: Proposes an Adaptive Causal Sampling Method (ACSM) that incorporates temporal causality into the sampling process by weighting the residual-based sampling probability with a causal term, preventing training failure in time-dependent PDEs.
Domain: PINN Adaptive Sampling Causal Training Time-Dependent PDEs

Is L2 Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network?

Date: 2022.06
Description: Theoretically proves that the standard L2 loss is unstable for training PINNs on high-dimensional HJB equations and proposes a new adversarial training algorithm to effectively minimize a more suitable L-infinity loss.
Domain: PINN Loss Function PDE Stability HJB Equation Adversarial Training

Robustness & Uncertainty Quantification:

A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regime

Date: 2019.07
Description: Proposes a physics-aware Bayesian framework using variational inference to construct coarse-grained models from sparse, high-dimensional data, enabling robust uncertainty quantification in the small data regime.
Domain: Probabilistic Modeling Uncertainty Quantification Bayesian Inference Coarse-Graining Small Data

Adversarial uncertainty quantification in physics-informed neural networks

Date: 2019.07
Description: Proposes a framework for uncertainty quantification in PINNs using deep generative models (VAEs and GANs), trained via an adversarial inference procedure where the generator is constrained by physical laws.
Domain: Uncertainty Quantification PINN Adversarial Inference GAN Probabilistic Modeling

B-PINNS: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

Date: 2020.10
Description: Proposes a Bayesian Physics-Informed Neural Network (B-PINN) framework that uses Hamiltonian Monte Carlo (HMC) or Variational Inference (VI) to infer the posterior distribution of network weights, enabling robust uncertainty quantification for PDE problems with noisy data.
Domain: Bayesian PINN Uncertainty Quantification Hamiltonian Monte Carlo Variational Inference Noisy Data

PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics

Date: 2021.06
Description: Proposes PID-GAN, a novel GAN framework where physics constraints are embedded into both the generator and the discriminator, enabling more robust and accurate uncertainty quantification for physical systems.
Domain: Uncertainty Quantification GAN PINN Probabilistic Modeling Adversarial Training

Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks

Date: 2021.08
Description: Proposes a physics-informed Wasserstein Generative Adversarial Network (WGAN) for uncertainty quantification, and provides a theoretical generalization error bound for the framework.
Domain: Uncertainty Quantification WGAN PINN Probabilistic Modeling Error Analysis

Flow Field Tomography with Uncertainty Quantification using a Bayesian Physics-Informed Neural Network

Date: 2021.08
Description: Proposes a Bayesian PINN framework for flow field tomography that reconstructs a 2D flow field from sparse line-of-sight data without boundary conditions, by incorporating both the measurement model and the Navier-Stokes equations into the loss function, while providing uncertainty quantification.
Domain: Bayesian PINN Uncertainty Quantification Inverse Problems Tomography Fluid Dynamics

Stochastic Physics-Informed Neural Ordinary Differential Equations

Date: 2021.09
Description: Proposes SPINODE, a framework that learns hidden physics in Stochastic Differential Equations (SDEs) by first deriving deterministic ODEs for the statistical moments, and then training a neural network within this moment-dynamics system using neural ODE solvers.
Domain: Stochastic Differential Equations Uncertainty Quantification Neural ODEs System Identification Probabilistic Modeling

A Physics-Data-Driven Bayesian Method for Heat Conduction Problems

Date: 2021.09
Description: Proposes a Heat Conduction Equation assisted Bayesian Neural Network (HCE-BNN) that embeds the PDE into the loss function of a BNN, enabling uncertainty quantification for forward and inverse heat conduction problems.
Domain: Bayesian PINN Uncertainty Quantification Bayesian Neural Network Heat Transfer

Spectral PINNS: Fast Uncertainty Propagation with Physics-Informed Neural Networks

Date: 2021.09
Description: Proposes Spectral PINNs, a method that learns the spectral coefficients of a Polynomial Chaos Expansion (PCE) of a stochastic PDE's solution, enabling fast uncertainty propagation by decoupling the spatiotemporal and stochastic domains.
Domain: Uncertainty Quantification Polynomial Chaos Expansion Stochastic PDEs Operator Learning

Multi-output physics-informed neural networks for forward and inverse PDE problems with uncertainties

Date: 2022.05
Description: Proposes a Multi-Output PINN (MO-PINN) that approximates the posterior distribution of the solution by training a single network with multiple output heads, each corresponding to a bootstrapped realization of the noisy data, enabling efficient uncertainty quantification.
Domain: Uncertainty Quantification PINN Bootstrap Multi-Output Network

Bayesian Physics Informed Neural Networks for real-world nonlinear dynamical systems

Date: 2022.07
Description: Extends the Bayesian PINN (B-PINN) framework to real-world nonlinear dynamical systems, such as biological growth and epidemic models, providing robust uncertainty quantification and inference of unobservable parameters from sparse, noisy data.
Domain: Bayesian PINN Uncertainty Quantification Dynamical Systems Epidemiology Biomechanics

Delta-PINNs: A new class of physics-informed neural networks for solving forward and inverse problems with noisy data

Date: 2022.10
Description: This paper introduces Delta-PINNs, a new training paradigm for PINNs designed to be highly robust to noisy data. Instead of minimizing the standard Mean Squared Error (MSE) of the PDE residuals, Delta-PINNs optimize a novel loss function based on the change ("Delta") of the mean of the residuals over training epochs. This approach focuses on driving the expectation of the residuals to zero in a monotonically decreasing fashion, effectively averaging out the effects of noise rather than fitting to it. The method demonstrates remarkable robustness, successfully solving forward and inverse problems even when the training data is corrupted with up to 100% noise.
Domain: PINN Robustness Noisy Data Loss Functions Scientific Machine Learning

Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks

Date: 2022.10
Description: This paper introduces a new class of PINNs designed to be robust against data with a high percentage of outliers. The authors first propose LAD-PINN, which replaces the standard Mean Squared Error (L2 norm) data loss with a Least Absolute Deviation (L1 norm) loss, making it inherently less sensitive to outliers. Building on this, they propose a two-stage MAD-PINN framework, which first uses LAD-PINN to identify and then screen out outliers based on the Median Absolute Deviation (MAD), and subsequently trains a standard PINN on the cleaned data for high accuracy. This approach is shown to be effective even when more than 50% of the data is corrupted.
Domain: PINN Robustness Outlier Detection Loss Functions Robust Regression

C.3.4 PINNs for Generalization: Learning Families of PDEs

Transfer Learning:

Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

Date: 2019.12
Description: Proposes a new variational energy-based PINN paradigm (VE-PINN) for more stable fracture problem solving, and innovatively uses transfer learning to significantly accelerate the sequential solving process under multiple load steps.
Domain: Variational PINN Phase-Field Fracture Transfer Learning Computational Acceleration

A physics-aware learning architecture with input transfer networks for predictive modeling

Date: 2020.08
Description: Proposes a novel hybrid architecture called OPTMA, whose core idea is to train a neural network to transform input features, enabling a simple "partial physics model" to make predictions matching a high-fidelity model.
Domain: Hybrid Modeling Transfer Learning Physics-Aware ML

Transfer learning based multi-fidelity physics informed deep neural network

Date: 2020.10
Description: Proposes the MF-PIDNN framework, which first pre-trains a network on approximate physical equations without data using the PINN method, and then fine-tunes the model with a few high-fidelity data points via transfer learning.
Domain: Multi-Fidelity PINN Transfer Learning Data-Efficient

Meta-Learning & Hypernetworks:

Meta-learning PINN loss functions

Date: 2021.07
Description: Proposes a gradient-based meta-learning framework to automatically discover an optimal, shared PINN loss function from a family of related PDE tasks, aiming to improve performance and efficiency on new tasks.
Domain: Meta-Learning PINN Loss Function Task Distribution

HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks

Date: 2021.10
Description: This paper introduces HyperPINN, a meta-learning framework that leverages hypernetworks to efficiently solve parameterized PDEs. Instead of training a new PINN for each parameter instance, HyperPINN trains a small "hypernetwork" that takes a physical parameter as input and outputs the weights for a smaller "main" PINN. This main network then solves the PDE for that specific parameter. This approach creates a single, compact model capable of instantly generating a specialized solver for any parameterization, offering a highly efficient and memory-saving alternative for multi-query and real-time applications.
Domain: PINN Meta-Learning Hypernetworks Parametric PDEs Scientific Machine Learning

A Meta learning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs

Date: 2021.10
Description: Proposes a model-aware metalearning approach that trains a surrogate model to learn the mapping from PDE parameters to optimal PINN initial weights, providing a high-quality starting point to accelerate training for new tasks.
Domain: Meta-Learning PINN Weight Initialization Parameterized PDEs

META-PDE: LEARNING TO SOLVE PDES QUICKLY WITHOUT A MESH

Date: 2022.11
Description: Proposes a framework called Meta-PDE that uses meta-learning (MAML/LEAP) to find an optimal PINN weight initialization, enabling rapid convergence in just a few gradient steps when solving new, related PDE tasks, even with varying geometries.
Domain: Meta-Learning PINN Model Initialization Fast PDE Solver

GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs

Date: 2023.03
Description: This paper introduces GPT-PINN, a novel meta-learning framework to drastically accelerate the solution of parametric PDEs for multi-query and real-time applications. It treats fully pre-trained PINNs, solved at adaptively selected parameter points, as activation functions or "neurons" in a hyper-reduced meta-network. This "network of networks" learns to generate solutions for new parameters by linearly combining a very small set of these pre-trained basis solutions. The framework is non-intrusive and results in an extremely lightweight and fast surrogate model.
Domain: PINN Meta-Learning Model Reduction Parametric PDEs Scientific Machine Learning

C.3.5 Theoretical Foundations, Convergence, and Failure Mode Analysis of PINNs

Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDES

Date: 2021.06
Description: Provides the first rigorous generalization error estimates for PINNs solving data assimilation (unique continuation) inverse problems by leveraging conditional stability estimates from classical PDE theory.
Domain: Generalization Error PINN Theory Inverse Problems Conditional Stability

Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs

Date: 2021.06
Description: Provides a comprehensive error analysis for PINNs approximating Kolmogorov PDEs, proving that the total error is bounded by the training error and that the required network size and sample complexity grow only polynomially with dimension.
Domain: Error Analysis PINN Theory Kolmogorov PDEs Curse of Dimensionality

Simultaneous Neural Network Approximations in Sobolev Spaces

Date: 2021.09
Description: Provides the first rigorous, non-asymptotic error bounds for deep ReLU networks approximating a smooth function and its derivatives simultaneously in Sobolev norms, establishing a key theoretical foundation for why PINNs are feasible.
Domain: Approximation Theory Neural Network Theory Sobolev Norms PINN Theory

Characterizing possible failure modes in physics-informed neural networks

Date: 2021.09
Description: Systematically identifies and characterizes key failure modes in PINN training, attributing them to "gradient pathologies" from imbalanced loss terms and "spectral bias" where networks fail to learn high-frequency components of the solution.
Domain: PINN Theory Failure Modes Gradient Pathologies Spectral Bias

Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

Date: 2021.09
Description: Identifies gradient pathologies, caused by imbalanced back-propagated gradients from different loss terms, as a key failure mode in PINNs and proposes a learning rate annealing algorithm that uses gradient statistics to adaptively balance the training.
Domain: PINN Theory Failure Modes Gradient Pathologies Loss Balancing Adaptive Training

Estimates on the generalization error of physics-informed neural networks for approximating PDEs

Date: 2022.01
Description: Provides rigorous upper bounds on the generalization error for PINNs approximating forward problems for a broad class of (nonlinear) PDEs by leveraging stability estimates of the underlying PDE.
Domain: Generalization Error PINN Theory Forward Problems PDE Stability

Investigating and Mitigating Failure Modes in Physics-informed Neural Networks (PINNs)

Date: 2022.09
Description: Identifies that high-order derivatives contaminate backpropagated gradients, causing training failure, and proposes a novel method to mitigate this by decomposing a high-order PDE into a first-order system using auxiliary variables.
Domain: PINN Failure Modes High-Order PDEs System Decomposition Gradient Contamination

C.3.6 Alternative Physics-Inspired Paradigms

Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling

Date: 2017.10
Description: This paper introduces Physics-Guided Neural Networks (PGNN), a framework that synergizes physics-based models and deep learning. PGNNs leverage the outputs of existing physics-based models as input features for a neural network. Crucially, they incorporate a physics-based loss function, which penalizes predictions that are inconsistent with known physical laws (e.g., density-temperature relationships in water) on a large set of unlabeled data. This approach ensures scientific consistency and significantly improves the model's generalization performance, especially in data-scarce scenarios.
Domain: Physics-Guided AI Hybrid Modeling PINN Alternatives Scientific Machine Learning Domain Knowledge Integration

DGM: A deep learning algorithm for solving partial differential equations

Date: 2018.08
Description: This paper introduces the Deep Galerkin Method (DGM), a pioneering deep learning framework for solving high-dimensional partial differential equations (PDEs). Similar to PINNs, DGM approximates the PDE solution with a neural network trained to satisfy the differential operator and boundary/initial conditions. Its key contribution lies in its meshfree nature, achieved by training on batches of randomly sampled points, which allows it to overcome the curse of dimensionality. The paper demonstrates DGM's effectiveness by accurately solving complex, high-dimensional free boundary PDEs in up to 200 dimensions.
Domain: PINN Deep Learning High-Dimensional PDEs Scientific Machine Learning Meshfree Methods

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

Date: 2018.11
Description: A novel framework that embeds physical laws, in the form of Stochastic Differential Equations (SDEs), into the architecture of a Generative Adversarial Network (GAN). This Physics-Informed GAN (PI-GAN) uses generators to model unknown stochastic processes (e.g., solution, coefficients), with some generators being induced by the SDE to enforce physical consistency. It provides a unified method for solving forward, inverse, and mixed stochastic problems from sparse data, and is capable of handling high-dimensional stochasticity.
Domain: Physics-Informed Machine Learning Generative Adversarial Networks Stochastic Differential Equations Inverse Problems Uncertainty Quantification

Convergence Rate of DeepONets for Learning Operators Arising from Advection-Diffusion Equations

Date: 2021.02
Description: Provides the first convergence rate analysis for DeepONets when learning solution operators for advection-diffusion equations, showing that the error depends polynomially on the input dimension and revealing the importance of the solution operator's structure.
Domain: DeepONet Operator Learning Convergence Rate Error Analysis

Variational physics informed neural networks: The role of quadratures and test functions

Date: 2021.06
Description: Provides a rigorous a priori error estimate for Variational PINNs (VPINNs) based on an inf-sup condition, revealing the counter-intuitive optimal strategy: using lowest-degree polynomial test functions with high-precision quadrature rules.
Domain: Variational PINN Error Analysis PINN Theory Inf-Sup Condition Petrov-Galerkin

SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs

Date: 2021.07
Description: This paper introduces Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) as a bridge between traditional meshless numerical methods and dense PINNs. Instead of a standard MLP, SPINN employs a sparse, shallow network where each hidden neuron's activation function is a learnable basis function (e.g., a radial basis function) inspired by classical function approximation theory. The network is trained using a physics-informed loss. This architecture is inherently sparse and offers partial interpretability, as the learned basis functions and their weights directly correspond to a classical solution expansion.
Domain: PINN Architecture Interpretability Sparse Neural Networks Meshfree Methods Scientific Machine Learning

Error Analysis of Deep Ritz Methods for Elliptic Equations

Date: 2021.07
Description: Provides the first rigorous, nonasymptotic convergence rate in the H1 norm for the Deep Ritz Method, establishing how network depth and width should be set relative to the number of training samples to achieve a desired accuracy.
Domain: Deep Ritz Method Error Analysis Convergence Rate Machine Learning Theory

Theory-guided hard constraint projection (HCP): A knowledge-based data-driven scientific machine learning method

Date: 2021.08
Description: This paper introduces the Theory-guided Hard Constraint Projection (HCP) framework, an alternative to the "soft constraint" approach of PINNs. HCP decouples data-driven learning from physics enforcement. First, a standard machine learning model makes a preliminary prediction based on data. Then, this prediction is "projected" onto a manifold representing the feasible solution space defined by physical laws. This two-step process mathematically guarantees that the final output strictly satisfies the imposed physical constraints, addressing a key limitation of soft-constraint methods and enhancing the scientific fidelity of the predictions.
Domain: Physics-Inspired AI Hard Constraints Constrained Optimization Scientific Machine Learning Hybrid Modeling

Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces

Date: 2021.08
Description: Proposes a data-driven method to learn the Green's functions of linear PDEs by framing the problem as functional linear regression in a Reproducing Kernel Hilbert Space (RKHS).
Domain: Operator Learning Reproducing Kernel Hilbert Space Green's Function Data-Driven Solver

A rate of convergence of physics informed neural networks for the linear second order elliptic PDEs

Date: 2021.09
Description: Provides a rigorous convergence rate analysis for PINNs solving second-order elliptic PDEs, establishing upper bounds on the required training samples, network depth, and width to achieve a desired accuracy by analyzing approximation and statistical errors.
Domain: PINN Theory Convergence Rate Error Analysis Rademacher Complexity

Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learning

Date: 2021.09
Description: This paper introduces Physics-Augmented Learning (PAL), a new paradigm to complement the popular Physics-Informed Learning (PIL) framework (e.g., PINNs). The authors draw a crucial distinction between "discriminative" physical properties (like PDEs, suitable for PIL's loss function) and "generative" properties (like conservation laws, which are hard to enforce as residuals). For generative properties, PAL proposes using them to augment a small initial dataset by generating a large number of new, physically-consistent pseudo-data points. This physics-based data augmentation allows neural networks to learn from generative physical laws that are inaccessible to the standard PINN approach.
Domain: Physics-Inspired AI Data Augmentation PINN Alternatives Scientific Machine Learning Generative Physics

Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems

Date: 2022.01
Description: This paper introduces Physics-informed graph neural Galerkin networks (PGN) to address the scalability and geometry-handling limitations of standard PINNs. The framework discretizes the problem domain into a graph (mesh) and employs a Graph Neural Network (GNN) to learn the solution at the graph nodes. Critically, its loss function is not based on the strong-form PDE residual, but is inspired by the weak-form Galerkin method from classical numerical analysis. This discrete, GNN-based approach significantly improves training efficiency and naturally handles irregular geometries with unstructured meshes.
Domain: PINN Architecture Graph Neural Networks Galerkin Method Scientific Machine Learning Discrete PINN

F. Future Direction

C.2 Symbolic System for Solving Physics Problems

C.2.0 General Surveys & Foundational Concepts

Machine learning and the physical sciences

Date: 2019.12
Description: This comprehensive review article systematically surveys the wide-ranging applications of machine learning in the physical sciences, exploring the current state, challenges, and future directions of the field.
Domain: Machine Learning Physics Review Statistical Physics Quantum Physics Particle Physics

AI meets physics: a comprehensive survey

Date: 2024.08
Description: This is a comprehensive survey of the 'AI meets physics' field, presenting a new PS4AI paradigm and classifying the intersection based on classical mechanics, electromagnetism, statistical physics, and quantum mechanics, while also outlining major challenges and future directions.
Domain: AI for Physics Physics-Inspired AI Survey Deep Learning

PARSING THE LANGUAGE OF EXPRESSION: ENHANCING SYMBOLIC REGRESSION WITH DOMAIN-AWARE SYMBOLIC PRIORS

Date: 2025.03
[cite_start]Description: Proposes an advanced symbolic regression method that extracts domain-specific "symbol priors" from scientific literature and integrates them into a novel tree-structured RNN to guide the discovery of expressions[cite: 2871].
Domain: Symbolic Regression Domain Knowledge Reinforcement Learning Neuro-Symbolic

C.2.1 Physics-Inspired Generative Models

Poisson Flow Generative Models

Date: 2022.12
Description: Proposes a novel generative modeling paradigm, Poisson Flow Generative Models (PFGM), that does not require a predefined prior noise distribution. It embeds the data manifold into a higher-dimensional space and constructs a vector field, derived from the solution to a classic Poisson PDE, that deterministically transports the data distribution to a uniform distribution on a hemisphere. To generate samples, one simply samples from this uniform distribution and solves the corresponding ODE backward in time. PFGM achieves state-of-the-art likelihood scores with extremely high sampling efficiency.
Domain: Generative Modeling Poisson Equation Continuous Normalizing Flows Physics-Inspired AI Differential Equations

Flow Matching for Generative Modeling

Date: 2023.02
Description: Introduces Flow Matching (FM), a new, simulation-free paradigm for training Continuous Normalizing Flows (CNFs) at scale. The method regresses a vector field that generates a predefined probability path from noise to data. Its core innovation, Conditional Flow Matching (CFM), makes the objective tractable and efficient by leveraging simple per-sample conditional paths. The paper also proposes using Optimal Transport (OT) paths, which are more efficient than standard diffusion paths, leading to faster training, faster sampling, and state-of-the-art performance on large-scale image generation tasks.
Domain: Generative Modeling Continuous Normalizing Flows Flow Matching Optimal Transport Diffusion Models

PFGM++: Unlocking the Potential of Physics-Inspired Generative Models

Date: 2023.02
Description: This paper introduces PFGM++, a new family of physics-inspired generative models that unifies and generalizes Poisson Flow Generative Models (PFGM) and diffusion models. By allowing the dimension D of the augmented space to be a flexible hyperparameter, PFGM++ can interpolate between the original PFGM (when D=1) and diffusion models (as D approaches infinity). The work also introduces an unbiased, perturbation-based training objective, resolving a key limitation of the original PFGM, and provides a method to transfer hyperparameters from well-tuned diffusion models. PFGM++ with intermediate D values is shown to achieve state-of-the-art results on image generation benchmarks.
Domain: Generative Modeling Poisson Flow Diffusion Models Physics-Inspired AI Unified Models

C.2.2 Quantum and Particle Physics

Searching for Exotic Particles in High-Energy Physics with Deep Learning

Date: 2014.02
Description: This seminal paper demonstrates that deep learning can significantly improve signal-versus-background classification in high-energy physics, outperforming traditional shallow methods without requiring manually-constructed features.
Domain: High Energy Physics Particle Physics Deep Learning Classification

Machine learning phases of matter

Date: 2016.05
Description: This paper demonstrates that supervised learning with neural networks and CNNs can effectively classify conventional and topological phases of matter directly from raw configurations, even without prior knowledge of the underlying physics.
Domain: Condensed Matter Physics Phase Transition Supervised Learning Ising Model

Discovering Phase Transitions with Unsupervised Learning

Date: 2016.06
Description: This paper pioneers the use of unsupervised learning, specifically PCA and clustering, to discover phases and phase transitions in the Ising model, demonstrating that machine learning can find fundamental physical concepts like order parameters without prior knowledge.
Domain: Unsupervised Learning Statistical Mechanics Phase Transition Ising Model

Learning phase transitions by confusion

Date: 2016.10
Description: This paper proposes a novel "confusion scheme" using neural networks and deliberately mislabeled data to detect phase transitions in physical systems without prior knowledge of order parameters.
Domain: Condensed Matter Physics Quantum Physics Phase Transition Machine Learning

Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations

Date: 2020.01
Description: A work demonstrating that an RNN (LSTM) can be trained to perform real-time, model-agnostic quantum filtering and reconstruct the full quantum state (including coherence) of an open superconducting qubit from experimental measurements.
Domain: Quantum Dynamics Quantum Control RNN/LSTM Superconducting Qubit

Graph Neural Networks in Particle Physics: Implementations, Innovations, and Challenges

Date: 2022.03
Description: A comprehensive review of the application of Graph Neural Networks (GNNs) in particle physics. This work highlights that physical systems like particle jets and detector signals can be naturally represented as graphs, making GNNs a particularly powerful and physically-motivated architecture. The paper surveys the successful use of GNNs across a wide range of tasks, including particle reconstruction, jet tagging, and event generation, demonstrating how this specialized architecture unlocks new capabilities in analyzing complex experimental data.
Domain: Graph Neural Networks Particle Physics AI for Science Experimental Data Analysis Scientific Machine Learning

Application of machine learning in solid state physics

Date: 2023.08
Description: A systematic review covering the application of ML models (RBM, ARNN, GNN, RL) to symbolic solid state and statistical physics problems, specifically focusing on multi-body systems, phase transitions, and ground state optimization (e.g., spin glasses).
Domain: Statistical Mechanics Phase Transition Spin Models Multi-Body Physics

From Architectures to Applications: A Review of Neural Quantum States

Date: 2024.02
Description: A comprehensive review of Neural Quantum States (NQS), detailing the architectures, training methods, and wide-ranging applications in simulating quantum many-body systems, from finding ground states to modeling quantum dynamics.
Domain: Neural Quantum States Quantum Many-Body Physics Variational Monte Carlo Computational Physics Review

Ultra-high-granularity detector simulation with intra-event aware generative adversarial network and self-supervised relational reasoning

Date: 2024.06
Description: Proposes IEA-GAN, a novel generative model using a Transformer-based relational reasoning module and self-supervised learning to achieve ultra-fast, high-fidelity simulation of high-granularity particle detectors.
Domain: Generative Models Particle Physics Detector Simulation Transformer Self-Supervised Learning

Neural-network quantum states for many-body physics

Date: 2024.08
Description: A methodological review of Neural Quantum States, deriving the core equations for Variational Monte Carlo approaches and emphasizing the role of the quantum geometric tensor in optimizing networks for many-body systems.
Domain: Neural Quantum States Quantum Many-Body Physics Variational Monte Carlo Computational Physics Review

Review of Machine Learning for Real-Time Analysis at the Large Hadron Collider experiments ALICE, ATLAS, CMS and LHCb

Date: 2025.06
Description: A comprehensive whitepaper reviewing the use of machine learning techniques for real-time data analysis and triggering systems in the major LHC experiments, highlighting methods for fast inference on hardware like FPGAs.
Domain: Machine Learning Particle Physics LHC Real-Time Analysis Trigger System

Solving the Hubbard model with Neural Quantum States

Date: 2025.07
Description: This work tackles the fundamental challenge of solving the Hubbard model, a cornerstone of condensed matter physics, by leveraging Neural Quantum States (NQS). The core innovation lies in parameterizing the quantum many-body wavefunction with an advanced neural network architecture inspired by Transformers, specifically incorporating a self-attention mechanism. This allows the NQS to efficiently capture the complex, long-range correlations and entanglement in strongly correlated electron systems. Optimized via the Variational Monte Carlo method, this approach achieves state-of-the-art accuracy in determining the ground state energy of the 2D Hubbard model, outperforming traditional numerical methods.
Domain: Neural Quantum States Hubbard Model Quantum Many-Body Physics Computational Physics AI for Science

Foundation Neural-Networks Quantum States as a Unified Ansatz for Multiple Hamiltonians

Date: 2025.08
Description: Introduces Foundation Neural-Network Quantum States (FNQS), a single, versatile Transformer-based architecture that takes Hamiltonian parameters as input, enabling it to generalize and solve for ground states of quantum systems unseen during training.
Domain: Neural Quantum States Foundation Models Quantum Many-Body Physics Meta-Learning Generalization

Advancing AI-Scientist Understanding: Multi-Agent LLMs with Interpretable Physics Reasoning

Date: 2025.08
Description: Introduces a multi-agent LLM framework that transforms free-form physics reasoning into an interpretable and executable model, enhancing reliability and human-AI collaboration.
Domain: Large Language Models Interpretability AI Scientist Multi-Agent Systems Human-AI Collaboration

C.2.3 Fluid Mechanics & Geosciences

Solving fluid flow problems using semi-supervised symbolic regression on sparse data

Date: 2019.11
Description: Uses semi-supervised symbolic regression to derive generalized fluid drag correlations from sparse data by incorporating known analytical solutions as prior knowledge to guide the model.
Domain: Symbolic Regression Fluid Mechanics Sparse Data Semi-Supervised Learning

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

Date: 2019.11
Description: Develops a physics-constrained DNN surrogate for parametric fluid flows that requires no simulation data for training, using the Navier-Stokes equations as the sole source of supervision and a novel architecture for hard boundary condition enforcement.
Domain: PINN Fluid Dynamics Surrogate Modeling Data-Free Learning Uncertainty Quantification

Physics-informed neural networks for high-speed flows

Date: 2019.12
Description: Applies PINNs to solve forward and inverse problems for the Euler equations in high-speed flows, demonstrating the ability to capture shocks and infer full flow fields from sparse, experimentally-inspired data like density gradients.
Domain: PINN Fluid Dynamics Euler Equations Shock Capturing Inverse Problem

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Date: 2020.02
Description: Introduces "Hidden Fluid Mechanics," a PINN framework that infers hidden velocity and pressure fields from visualized scalar concentration data by embedding the Navier-Stokes equations as a physical constraint.
Domain: PINN Fluid Dynamics Inverse Problem Data Assimilation Flow Visualization

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

Date: 2020.11
Description: Systematically investigates PINNs for solving the incompressible Navier-Stokes equations by comparing velocity-pressure (VP) and vorticity-velocity (VV) formulations, and presents a pioneering attempt at direct turbulence simulation.
Domain: PINN Fluid Dynamics Navier-Stokes Turbulence Inverse Problem

Prediction of porous media fluid flow using physics informed neural networks

Date: 2021.07
Description: Applies PINNs to the Buckley-Leverett problem for two-phase flow in porous media, demonstrating superior extrapolation capabilities over standard ANNs and the ability to solve inverse problems for multiphase flow parameters.
Domain: PINN Porous Media Flow Reservoir Engineering Buckley-Leverett Inverse Problem

Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks

Date: 2022.09
Description: Proposes a sequential PINN solver for complex thermo-hydro-mechanical (THM) inverse problems in porous media by decoupling the multiphysics system and training separate networks in sequence.
Domain: PINN Poromechanics Geosciences Inverse Problem Multiphysics

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

Date: 2023.04
Description: A framework coupling LBM fluid flow and PHREEQCRM geochemical solvers, featuring an AI (ANN/MLP) optimization workflow for automatically calibrating reaction constants (log K) in complex pore-scale reactive transport models without domain knowledge.
Domain: Fluid Mechanics/LBM Geosciences Pore-Scale Modeling AI Optimization/ANN

ASP-Assisted Symbolic Regression: Uncovering Hidden Physics in Fluid Mechanics

Date: 2025.07
Description: Proposes a hybrid framework combining Symbolic Regression (SR) to discover physical equations and Answer Set Programming (ASP) to enforce domain-specific constraints, ensuring physical plausibility.
Domain: Symbolic Regression Knowledge Representation Fluid Mechanics AI for Science

Machine learning-enhanced fully coupled fluid-solid interaction models for proppant dynamics in hydraulic fractures

Date: 2025.08
Description: Proposes a hybrid framework that uses first-principles symbolic physics equations to generate synthetic data for training a high-accuracy stacked ensemble machine learning model to predict proppant settling in hydraulic fractures.
Domain: Symbolic Physics Ensemble Learning Fluid-Solid Interaction Hydraulic Fracturing

C.2.4 Solid Mechanics & Materials Science

Symbolic regression in materials science

Date: 2019.01
Description: Introduces and advocates for symbolic regression as an interpretable machine learning alternative for discovering governing physical laws and structure-property relationships from materials data.
Domain: Symbolic Regression Materials Informatics Genetic Programming Scientific Discovery

Recent advances and applications of machine learning in solid-state materials science

Date: 2019.08
Description: This review provides a comprehensive overview of the latest advancements in applying machine learning to solid-state materials science, covering material discovery, property prediction, force fields, and key challenges like interpretability and data scarcity.
Domain: Materials Science Review Machine Learning Solid State Physics

Theory-training deep neural networks for an alloy solidification benchmark problem

Date: 2019.12
Description: Presents the first application of PINNs to alloy solidification, demonstrating the ability to solve coupled phase-change equations and learn implicit variables like solid fraction without any simulation data.
Domain: PINN Materials Science Solidification Phase Change Thermodynamics

Machine Learning Approaches to Predicting and Understanding the Mechanical Properties of Steels

Date: 2020.03
Description: Employs Random Forest and Symbolic Regression to not only predict the mechanical properties of steels but also to identify key influencing features and discover interpretable mathematical formulas for materials design.
Domain: Symbolic Regression Random Forest Materials Informatics Feature Selection

A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity

Date: 2021.08
Description: First applies PINNs to solve fourth-order biharmonic equations in elasticity by constructing a novel "Airy-Network" whose architecture is directly guided by classical analytical solutions (e.g., Airy stress functions), leading to superior accuracy and efficiency over standard PINNs.
Domain: PINN Solid Mechanics Elasticity Theory Biharmonic Equation Feature Engineering

Physics-informed neural networks for the shallow-water equations on the sphere

Date: 2022.02
Description: Solves the shallow-water equations on a sphere using a novel multi-model approach, where the time domain is decomposed and a sequence of PINNs are trained to handle long integration intervals, a key challenge for standard PINNs.
Domain: PINN Geophysical Fluid Dynamics Shallow-Water Equations Domain Decomposition Meteorology

Hierarchical symbolic regression for identifying key physical parameters correlated with bulk properties of perovskites

Date: 2022.02
Description: Proposes a hierarchical symbolic regression framework (hiSISSO) to efficiently discover complex analytical models for materials properties and transfer knowledge between different physical properties.
Domain: Symbolic Regression Materials Informatics Compressed Sensing Perovskites

A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: Comparison with finite element method

Date: 2022.09
Description: Proposes a novel mixed formulation for PINNs, inspired by FEM, that uses separate networks for the primary variable and its spatial gradient and combines energy-based and strong-form losses to accurately solve problems in heterogeneous solids while avoiding high-order derivatives.
Domain: PINN Mixed Formulation Finite Element Method Solid Mechanics Heterogeneous Materials

A physically consistent framework for fatigue life prediction using probabilistic physics-informed neural network

Date: 2022.09
Description: Proposes a probabilistic PINN for fatigue life prediction that ensures physical consistency by encoding fatigue principles (e.g., S-N curve monotonicity and heteroscedasticity) as first and second-order derivative constraints in the loss function.
Domain: PINN Solid Mechanics Fatigue Life Prediction Probabilistic Modeling Uncertainty Quantification

Neuro - symbolic Al for materials modelling and processes design

Date: 2024.01
Description: Proposes a hybrid neuro-symbolic framework to improve materials modeling by using symbolic AI rules to optimize the design and training of Artificial Neural Networks (ANNs) and to interpret their results.
Domain: Neuro-Symbolic Artificial Neural Network Materials Science Ontology

Combining genetic algorithm and compressed sensing for features and operators selection in symbolic regression

Date: 2024.03
Description: Proposes a GA-SISSO framework where a Genetic Algorithm is used as a wrapper to select optimal subsets of features and operators for the SISSO symbolic regression algorithm, overcoming its computational bottleneck with large feature spaces.
Domain: Symbolic Regression Genetic Algorithm Feature Selection Materials Informatics

State-of-the-art review on the use of AI-enhanced computational mechanics in geotechnical engineering

Date: 2024.07
Description: This state-of-the-art review comprehensively analyzes the use of AI-enhanced computational mechanics in geotechnical engineering, categorizing applications and identifying future research directions, particularly the integration of physically-guided and adaptive learning.
Domain: Geotechnical Engineering Computational Mechanics Solid Mechanics Review

A Multi-agent Framework for Materials Laws Discovery

Date: 2024.11
Description: Proposes a multi-agent framework based on Large Language Models (LLMs) that uses a depth-first search with memory and reflection mechanisms to perform symbolic regression and discover interpretable laws in materials science.
Domain: Large Language Model Multi-agent System Symbolic Regression Materials Science

DEM-NeRF: A Neuro-Symbolic Method for Scientific Discovery through Physics-Informed Simulation

Date: 2025.07
Description: Proposes a novel neuro-symbolic framework (DEM-NeRF) that integrates Neural Radiance Fields (NeRF) for 3D reconstruction from images with a Deep Energy Method (DEM) PINN to simulate hyperelastic object deformation in real-time.
Domain: Neuro-Symbolic Neural Radiance Field Physics-Informed Neural Network Solid Mechanics

C.2.5 Energy Systems & Thermodynamics

Lattice Thermal Conductivity Prediction using Symbolic Regression and Machine Learning

Date: 2020.08
Description: Uses symbolic regression to discover four new, interpretable formulas for lattice thermal conductivity that outperform the classic Slack model, and rigorously compares the poor extrapolation performance of SR and black-box ML models.
Domain: Symbolic Regression Thermal Conductivity Materials Informatics Extrapolation

Physics-Informed Neural Networks for AC Optimal Power Flow

Date: 2022.07
Description: First applies PINNs to the AC-OPF problem by incorporating KKT optimality conditions into the loss function, and introduces formal verification methods to provide rigorous worst-case guarantees on constraint violations.
Domain: PINN Power Systems Optimal Power Flow Worst-case Guarantees Energy Systems

A Physics-Informed Machine Learning Approach for Estimating Lithium-Ion Battery Temperature

Date: 2022.08
Description: Applies a PINN with a novel architecture and adaptive loss to predict lithium-ion battery temperature using a lumped thermal model and sparse data.
Domain: PINN Energy Systems Battery Management Thermodynamics Data-driven Modeling

Physics-Informed Neural Network for Discovering Systems with Unmeasurable States with Application to Lithium-Ion Batteries

Date: 2023.11
Description: Proposes a novel PINN training method that embeds a numerical solver for the governing equations into the forward pass of the loss function, enabling the discovery of unmeasurable internal states in complex systems like Li-ion batteries from observable data alone.
Domain: PINN System Identification Unmeasurable States Differentiable Physics Energy Systems

PE-GPT: A Physics-Informed Interactive Large Language Model for Power Converter Modulation Design

Date: 2024.03
Description: This paper introduces PE-GPT, a novel system that synergizes a Large Language Model (LLM) with Physics-Informed Neural Networks (PINNs) to create an interactive design assistant for power electronics. The LLM (GPT-4) acts as a natural language interface, guiding users through the design process via in-context learning. The backend consists of a custom, hierarchical PINN architecture that accurately models the converter's physics with high data efficiency. This framework significantly enhances the accessibility, explainability, and efficiency of the power converter modulation design process.
Domain: Large Language Models Physics-Informed Neural Networks Human-AI Interaction Engineering Design Power Electronics

Recent progress of artificial intelligence for liquid-vapor phase change heat transfer

Date: 2024.03
Description: This review provides a comprehensive overview of how AI and machine learning are revolutionizing liquid-vapor phase change heat transfer research by enabling advanced meta-analysis, physical feature extraction from visual data, and real-time data stream analysis for smart thermal systems.
Domain: Phase Change Heat Transfer AI for Physics Review

Mapping the design of electrolyte additive for stabilizing zinc anode in aqueous zinc ion batteries

Date: 2024.03
Description: This review article systematically classifies and analyzes the mechanisms of electrolyte additives for stabilizing zinc anodes in aqueous zinc-ion batteries, highlighting how AI and ML can accelerate the discovery and design of next-generation battery technologies.
Domain: Zinc-ion Batteries Electrochemistry Energy Storage Review

Interpretable data-driven turbulence modeling for separated flows using symbolic regression with unit constraints

Date: 2024.05
Description: Proposes a novel framework for turbulence modeling that uses unit-constrained symbolic regression to learn interpretable, physically consistent corrections for RANS models to improve predictions of separated flows.
Domain: Symbolic Regression Turbulence Modeling Unit Constraints Separated Flow

Physics-informed neural network for lithium-ion battery degradation stable modeling and prognosis

Date: 2024.05
Description: Proposes a PINN for battery state-of-health (SOH) prognosis by learning the single-cycle degradation dynamics constrained by an empirical state-space degradation model.
Domain: PINN Energy Systems Battery Management State of Health Prognosis

KnowTD an actionable knowledge representation system for thermodynamics

Date: 2024.07
Description: Presents KnowTD, a novel "machine teaching" system that uses a formal ontology and a reasoner to represent thermodynamic knowledge and autonomously solve introductory-level problems with explainable, guaranteed-correct steps.
Domain: Symbolic AI Knowledge Representation Ontology Thermodynamics Expert System

Large Language Model Driven Development of Turbulence Models

Date: 2025.05
Description: Demonstrates a new paradigm where a Large Language Model (LLM) acts as a collaborative agent to autonomously propose, reason about, and refine interpretable turbulence wall models for complex flows.
Domain: Large Language Model AI Agent Turbulence Modeling Fluid Mechanics

Recent Advances in CO (2) Electroreduction Driven by Artificial Intelligence and Machine Learning

Date: 2025.09
Description: This review provides a comprehensive survey of how AI and ML are driving the field of CO₂ electroreduction, focusing on catalyst design, reaction mechanism investigation, and knowledge graph construction to accelerate the discovery of sustainable energy materials.
Domain: Electrocatalysis CO2 Reduction Generative AI Energy Systems

C.2.6 Interdisciplinary & Complex Systems

Deep Learning for Plasma Tomography and Disruption Prediction from Bolometer Data

Date: 2020.06
Description: Utilizes Convolutional Neural Networks (CNNs) for real-time plasma radiation tomography and Recurrent Neural Networks (RNNs) for disruption prediction from bolometer data in the JET tokamak.
Domain: Deep Learning Plasma Physics Nuclear Fusion Tomography Disruption Prediction

PHYSICS-INFORMED NEURAL NETWORK FOR NONLINEAR DYNAMICS IN FIBER OPTICS

Date: 2021.09
Description: Develops a generalizable PINN for the Nonlinear Schrödinger Equation by embedding physical parameters (e.g., pulse power) as inputs, enabling a single model to solve multiple fiber optic dynamics scenarios.
Domain: PINN Nonlinear Optics Fiber Optics NLSE Generalizability

Investigating a New Approach to Quasinormal Modes: Physics-Informed Neural Networks

Date: 2021.08
Description: Pioneers the use of PINNs for calculating black hole quasinormal modes by framing the problem of finding the unknown quasinormal frequency as an inverse parameter identification problem within the perturbation equation.
Domain: PINN Black Hole Physics General Relativity Quasinormal Modes Inverse Problem

Towards neural Earth system modelling by integrating artificial intelligence in Earth system science

Date: 2021.08
Description: Proposes the concept of 'neural Earth system modelling' (NESYM), a methodological vision for deeply integrating AI and Earth System Models (ESMs) into learning, self-validating, and interpretable hybrids to tackle grand challenges in climate science.
Domain: Earth System Science Climate Modeling AI for Science Hybrid Modeling Review

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

Date: 2021.10
Description: Proposes a novel 'explicit' PINN approach for upscaling, where a neural network learns the nonlinear closure term (effectiveness factor) by explicitly using macroscale variables (concentration and its gradient) as input features, demonstrating excellent generalizability for transport in complex biological tissues.
Domain: PINN Multiscale Modeling Upscaling Nonlinear Closure Biophysics

Physically guided deep learning solver for time-dependent Fokker-Planck equation

Date: 2022.08
Description: Proposes a PINN-based solver for the Fokker-Planck equation, uniquely using dropout during inference to assess model robustness and demonstrating that sparse observation data can effectively substitute for missing boundary conditions.
Domain: PINN Fokker-Planck Equation Stochastic Dynamics Robustness

Deep learning for intrinsically disordered proteins: From improved predictions to deciphering conformational ensembles

Date: 2024.07
Description: Reviews the impact of deep learning on the study of intrinsically disordered proteins (IDPs), highlighting the shift from predicting disordered regions to using generative models for deciphering their complex conformational ensembles.
Domain: Deep Learning Biophysics Structural Biology Intrinsically Disordered Proteins Generative Models

SpecCLIP: Aligning and Translating Spectroscopic Measurements for Stars

Date: 2025.07
Description: A CLIP-inspired foundation model for stellar spectral analysis that leverages cross-instrument contrastive pre-training and spectrum-aware decoders to enable precise spectral alignment, parameter estimation, and anomaly detection across diverse astronomical applications.
Domain: Contrastive Learning Astrophysics

5. Cross Domain Applications and Future Directions

5.2 Others (Healthcare, Biophysics, Architecture, Aerospace Science, Education)

Achieving Precise and Reliable Locomotion with Differentiable Simulation-Based System Identification

Date: 2025.08
Description: It combines system identification with RL training to optimize physical parameters from trajectory data, achieving 75% reduction in rotational drift and 46% improvement in directional movement for bipedal locomotion compared to baseline methods.
Domain: Robotics Differentiable Simulator

Calibrating Biophysical Models for Grape Phenology Prediction via Multi-Task Learning

Date: 2025.08
Description: It proposes a hybrid modeling approach that combines multi-task learning with a recurrent neural network to parameterize a differentiable biophysical model. This method significantly outperforms both conventional biophysical models and baseline deep learning approaches in predicting phenological stages, as well as other crop state variables such as cold-hardiness and wheat yield.
Domain: Graph Neural Networks Biophysical Model

HeartUnloadNet: A Weakly-Supervised Cycle-Consistent Graph Network for Predicting Unloaded Cardiac Geometry from Diastolic States

Date: 2025.07
Description: HeartUnloadNet is a deep learning framework that predicts unloaded left ventricular (LV) shape directly from end-diastolic (ED) meshes while explicitly incorporating biophysical priors. The network accepts meshes of arbitrary size and physiological parameters such as ED pressure, myocardial stiffness, and fiber helicity orientation, and outputs the corresponding unloaded mesh. It employs a graph attention architecture and a cycle consistency strategy for bidirectional (loaded and unloaded) prediction, enabling partial self-supervision, which improves accuracy and reduces the need for large training datasets.
Domain: Graph Neural Networks Biophysical Model

The AlphaPhysics Term Rewriting System for Marking Algebraic Expressions in Physics Exams

Date: 2025.08
Description: This automated physics grading system integrates LLM preprocessing with dual verification pathways (general SMT solvers and physics-specific term rewriting), successfully processing 1500+ Olympiad exam responses by combining natural language understanding with formal mathematical validation of student solutions.
Domain: Agent Physics Grading

Creating a customisable freely-accessible Socratic AI physics tutor

Date: 2025.07
Description: It customizes Gemini into a physics tutor that promotes Socratic dialogue rather than direct answers, successfully guiding students through diagram analysis and conceptual reasoning while acknowledging persistent limitations in accuracy.
Domain: Agent Physics Tutor

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Awesome AI for Physics

💥 News

📖 Content

1. Physical Perception

1.1 Object Recognition

1.2 Spatial Perception

1.3 Identifying Intrinsic Property

1.4 Dynamic Estimation

1.5 Causal and Counterfactual Inference

2. Physics Reasoning

2.1 Database (Dataset and benchmarks)

SciCode: A Research Coding Benchmark Curated by Scientists:

2.2 General Physics Reasoning Models

2.3 Theoretical Physics Solvers

3. World Model

3.1 Generative Models

3.2 Physics and Physical Engine

3.3 Physics-enhanced Modeling Approaches.

3.4 Benchmarking Modeling Capability

4. Embodied Interaction

4.1 Robotics

4.2 Navigation

4.3 Autonomous Driving