mlsanityData to 7 Oct 2026

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

arXiv 2203.16797 ↗First posted 31 Mar 2022cs.LG stat.MLcited by 64

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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.

Key facts. Cited by 64 papers in the map (data through 7 Oct 2026). Builds on 125 of its 216 references that are in the map. First posted on arXiv 31 Mar 2022.

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125 of 216 references.

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Citing papers per year: 2022: 2; 2023: 12; 2024: 10; 2025: 27; 2026: 13.

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  1. 2023Physics-Informed Computer Vision: A Review and Perspectivescited by 28
  2. 2023A Survey on Physics Informed Reinforcement Learning: Review and Open Problemscited by 22
  3. 2023Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlookcited by 11
  4. 2023Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equationscited by 10
  5. 2023Meta-learning in healthcare: A surveycited by 9
  6. 2024Parametric Encoding with Attention and Convolution Mitigate Spectral Bias of Neural Partial Differential Equation Solverscited by 9
  7. 2022Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNscited by 8
  8. 2024Reasoning-Enhanced Object-Centric Learning for Videoscited by 7
  9. 2025Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Modelscited by 7
  10. 2023Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networkscited by 6
  11. 2024PINNs for Medical Image Analysis: A Surveycited by 5
  12. 2025SlotPi: Physics-informed Object-centric Reasoning Modelscited by 5
38 more
  1. 2025Physics-Constrained Machine Learning for Chemical Engineeringcited by 5
  2. 2022Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilationcited by 4
  3. 2024PAPM: A Physics-aware Proxy Model for Process Systemscited by 4
  4. 2025Structure is information: structural identifiability mappings for machine learning with partially observed dynamical systemscited by 4
  5. 2023Estimating Treatment Effects in Continuous Time with Hidden Confounderscited by 3
  6. 2023Inductive biases in deep learning models for weather predictioncited by 3
  7. 2025Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sourcescited by 3
  8. 2023KARNet: Kalman Filter Augmented Recurrent Neural Network for Learning World Models in Autonomous Driving Taskscited by 2
  9. 2024A Review of Physics-Informed Machine Learning Methods with Applications to Condition Monitoring and Anomaly Detectioncited by 2
  10. 2024Bayesian Differentiable Physics for Cloth Digitalizationcited by 2
  11. 2025Data Readiness for Scientific AI at Scalecited by 2
  12. 2025Physics-Informed Diffusion Models for Unsupervised Anomaly Detection in Multivariate Time Seriescited by 2
  13. 2025Incomplete Data, Complete Dynamics: A Diffusion Approachcited by 2
  14. 2025Convergence and Sketching-Based Efficient Computation of Neural Tangent Kernel Weights in Physics-Based Losscited by 2
  15. 2026PhyMix: Towards Physically Consistent Single-Image 3D Indoor Scene Generation with Implicit--Explicit Optimizationcited by 2
  16. 2026Autoregression-Free Neural Operators for Time-Dependent PDEscited by 2
  17. 2023On Training Derivative-Constrained Neural Networkscited by 1
  18. 2023Interpretable Neural PDE Solvers using Symbolic Frameworkscited by 1
  19. 2024Link Prediction with Physics-Inspired Graph Neural Networkscited by 1
  20. 2024sEMG-Driven Physics-Informed Gated Recurrent Networks for Modeling Upper Limb Multi-Joint Movement Dynamicscited by 1
  21. 2025BO-SA-PINNs: Self-adaptive physics-informed neural networks based on Bayesian optimization for automatically designing PDE solverscited by 1
  22. 2025Superstudent intelligence in thermodynamicscited by 1
  23. 2025Gradient Enhanced Self-Training Physics-Informed Neural Network (gST-PINN) for Solving Nonlinear Partial Differential Equationscited by 1
  24. 2025Multi-resolution Physics-Aware Recurrent Convolutional Neural Network for Complex Flowscited by 1
  25. 2026Learning and extrapolating scale-invariant processescited by 1
  26. 2026Controlled oscillation modeling using port-Hamiltonian neural networkscited by 1
  27. 2026TRIE: An Evaluation Framework for Stochastic PDE Surrogatescited by 1
  28. 2023Bayesian Reasoning for Physics Informed Neural Networkscited by 0
  29. 2024Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEscited by 0
  30. 2024SPIN: SE(3)-Invariant Physics Informed Network for Binding Affinity Predictioncited by 0
  31. 2025Deep Muscle EMG construction using A Physics-Integrated Deep Learning approachcited by 0
  32. 2025Constraint-Guided Learning of Data-driven Health Indicator Models: An Application on the Pronostia Bearing Datasetcited by 0
  33. 2025LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSEcited by 0
  34. 2025Scientific machine learning in Hydrology: a unified perspectivecited by 0
  35. 2025Knowledge-Guided Machine Learning: Illustrating the use of Explainable Boosting Machines to Identify Overshooting Tops in Satellite Imagerycited by 0
  36. 2025Physics-Informed Multimodal Bearing Fault Classification under Variable Operating Conditions using Transfer Learningcited by 0
  37. 2025Hybrid Fourier Neural Operator-Plasma Fluid Model for Fast and Accurate Multiscale Simulations of High Power Microwave Breakdowncited by 0
  38. 2025Training Variation of Physically-Informed Deep Learning Modelscited by 0

50 most cited of 64 All 64 (JSON)