# When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning

arXiv: https://arxiv.org/abs/2203.16797 · HTML: https://mlsanity.com/paper/2203.16797/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- Builds on 125 of its 216 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 30 of 125)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Convolutional Neural Networks for Sentence Classification](https://mlsanity.com/paper/1408.5882/) (2014)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)

## Built on by (most cited first, 30 of 65)

- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [A Survey on Physics Informed Reinforcement Learning: Review and Open Problems](https://mlsanity.com/paper/2309.01909/) (2023)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equations](https://mlsanity.com/paper/2303.02304/) (2023)
- [Meta-learning in healthcare: A survey](https://mlsanity.com/paper/2308.02877/) (2023)
- [Parametric Encoding with Attention and Convolution Mitigate Spectral Bias of Neural Partial Differential Equation Solvers](https://mlsanity.com/paper/2403.15652/) (2024)
- [Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs](https://mlsanity.com/paper/2210.03426/) (2022)
- [Reasoning-Enhanced Object-Centric Learning for Videos](https://mlsanity.com/paper/2403.15245/) (2024)
- [Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models](https://mlsanity.com/paper/2509.03036/) (2025)
- [Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks](https://mlsanity.com/paper/2308.02137/) (2023)
- [Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation](https://mlsanity.com/paper/2209.15609/) (2022)
- [PINNs for Medical Image Analysis: A Survey](https://mlsanity.com/paper/2408.01026/) (2024)
- [SlotPi: Physics-informed Object-centric Reasoning Models](https://mlsanity.com/paper/2506.10778/) (2025)
- [Physics-Constrained Machine Learning for Chemical Engineering](https://mlsanity.com/paper/2508.20649/) (2025)
- [PAPM: A Physics-aware Proxy Model for Process Systems](https://mlsanity.com/paper/2407.05232/) (2024)
- [Structure is information: structural identifiability mappings for machine learning with partially observed dynamical systems](https://mlsanity.com/paper/2502.04131/) (2025)
- [Estimating Treatment Effects in Continuous Time with Hidden Confounders](https://mlsanity.com/paper/2302.09446/) (2023)
- [Inductive biases in deep learning models for weather prediction](https://mlsanity.com/paper/2304.04664/) (2023)
- [Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sources](https://mlsanity.com/paper/2508.19847/) (2025)
- [Incomplete Data, Complete Dynamics: A Diffusion Approach](https://mlsanity.com/paper/2509.20098/) (2025)
- [KARNet: Kalman Filter Augmented Recurrent Neural Network for Learning World Models in Autonomous Driving Tasks](https://mlsanity.com/paper/2305.14644/) (2023)
- [A Review of Physics-Informed Machine Learning Methods with Applications to Condition Monitoring and Anomaly Detection](https://mlsanity.com/paper/2401.11860/) (2024)
- [Bayesian Differentiable Physics for Cloth Digitalization](https://mlsanity.com/paper/2402.17664/) (2024)
- [Data Readiness for Scientific AI at Scale](https://mlsanity.com/paper/2507.23018/) (2025)
- [Physics-Informed Diffusion Models for Unsupervised Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2508.11528/) (2025)
- [Convergence and Sketching-Based Efficient Computation of Neural Tangent Kernel Weights in Physics-Based Loss](https://mlsanity.com/paper/2511.15530/) (2025)
- [PhyMix: Towards Physically Consistent Single-Image 3D Indoor Scene Generation with Implicit--Explicit Optimization](https://mlsanity.com/paper/2604.10125/) (2026)
- [Autoregression-Free Neural Operators for Time-Dependent PDEs](https://mlsanity.com/paper/2605.25413/) (2026)
- [TRIE: An Evaluation Framework for Stochastic PDE Surrogates](https://mlsanity.com/paper/2607.00196/) (2026)
- [On Training Derivative-Constrained Neural Networks](https://mlsanity.com/paper/2310.01649/) (2023)

## Abstract (arXiv)

Physics-informed machine learning (PIML), referring to the combination of prior knowledge of physics, which is the high level abstraction of natural phenomenons and human behaviours in the long history, with data-driven machine learning models, has emerged as an effective way to mitigate the shortage of training data, to increase models' generalizability and to ensure the physical plausibility of results. In this paper, we survey an abundant number of recent works in PIML and summarize them from three aspects: (1) motivations of PIML, (2) physics knowledge in PIML, (3) methods of physics knowledge integration in PIML. We also discuss current challenges and corresponding research opportunities in PIML.