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Physics-Guided Deep Learning for Dynamical Systems: A Survey

arXiv 2107.01272 ↗First posted 2 Jul 2021cs.LGcited by 43

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Abstract (arXiv)

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation is usually computationally intensive, requiring significant computational resources and expertise, and many real-world systems do not have fully-known governing laws. While deep learning (DL) provides novel alternatives for efficiently recognizing complex patterns and emulating nonlinear dynamics, its predictions do not necessarily obey the governing laws of physical systems, nor do they generalize well across different systems. Thus, the study of physics-guided DL emerged and has gained great progress. Physics-guided DL aims to take the best from both physics-based modeling and state-of-the-art DL models to better solve scientific problems. In this paper, we provide a structured overview of existing methodologies of integrating prior physical knowledge or physics-based modeling into DL, with a special emphasis on learning dynamical systems. We also discuss the fundamental challenges and emerging opportunities in the area.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). Builds on 112 of its 236 references that are in the map. First posted on arXiv 2 Jul 2021.

Builds on

112 of 236 references.

References · 112

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50 most cited of 112 All 112 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 9; 2024: 9; 2025: 9; 2026: 11.

43 papers.

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  2. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  3. 2024When are dynamical systems learned from time series data statistically accurate?cited by 14
  4. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  5. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  6. 2024Full Shot Predictions for the DIII-D Tokamak via Deep Recurrent Networkscited by 9
  7. 2025PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systemscited by 9
  8. 2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
  9. 2023Physics-Regulated Deep Reinforcement Learning: Invariant Embeddingscited by 8
  10. 2023Approaching epidemiological dynamics of COVID-19 with physics-informed neural networkscited by 7
  11. 2022Deep Grey-Box Modeling With Adaptive Data-Driven Models Toward Trustworthy Estimation of Theory-Driven Modelscited by 6
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31 more
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  3. 2023Out of Distribution Detection via Domain-Informed Gaussian Process State Space Modelscited by 3
  4. 2024Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditionscited by 3
  5. 2025Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networkscited by 3
  6. 2025Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Modelscited by 3
  7. 2023CONFIDE: Contextual Finite Differences Modelling of PDEscited by 2
  8. 2023Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing datacited by 2
  9. 2024Mitigating distribution shift in machine learning-augmented hybrid simulationcited by 2
  10. 2026From Sparse Sensors to Continuous Fields: STRIDE for Spatiotemporal Reconstructioncited by 2
  11. 2026Rethinking Input Domains in Physics-Informed Neural Networks via Geometric Compactification Mappingscited by 2
  12. 2026Adaptive Symmetry Discovery for Dynamical System Identificationcited by 2
  13. 2021Latent Space Simulation for Carbon Capture Design Optimizationcited by 1
  14. 2023PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learningcited by 1
  15. 2024Data-driven discovery of self-similarity using neural networkscited by 1
  16. 2024Guiding Video Prediction with Explicit Procedural Knowledgecited by 1
  17. 2025Physics Informed Constrained Learning of Dynamics from Static Datacited by 1
  18. 2025A Physiologically-Constrained Neural Network Digital Twin Framework for Replicating Glucose Dynamics in Type 1 Diabetescited by 1
  19. 2026PnP-Corrector: A Universal Correction Framework for Coupled Spatiotemporal Forecastingcited by 1
  20. 2026DBPnet: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Wheel Load Estimationcited by 1
  21. 2026Physics-Informed Modeling for Wood Thermal Analysis and Predictioncited by 1
  22. 2023Scientific Computing Algorithms to Learn Enhanced Scalable Surrogates for Mesh Physicscited by 0
  23. 2023Physics-Enhanced TinyML for Real-Time Detection of Ground Magnetic Anomaliescited by 0
  24. 2025Generalizing to New Dynamical Systems via Frequency Domain Adaptationcited by 0
  25. 2025Control-Augmented Autoregressive Diffusion for Data Assimilationcited by 0
  26. 2025Conditional Clifford-Steerable CNNs for PDE Modelingcited by 0
  27. 2026Generalizing Dynamics Modeling More Easily from Representation Perspectivecited by 0
  28. 2026Pure and physics-guided deep learning approaches for spatio-temporal groundwater level predictioncited by 0
  29. 2026Hybrid Quantum-Classical PINNs for Scientific Computing: A Multi-GPU Open-Source Frameworkcited by 0
  30. 2026Dual-Network PINNs for Optimal Control: A Reproducible Benchmark on the Mass-Spring-Damper Systemcited by 0
  31. 2026LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systemscited by 0