mlsanityData to 7 Oct 2026

Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge

arXiv 1711.07970 ↗First posted 21 Nov 2017cs.AI cs.LG stat.MLcited by 95

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Abstract (arXiv)

We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge more traditional approaches elaborated over the years in fields like maths or physics. However, despite considerable successes in a variety of application domains, the machine learning field is not yet ready to handle the level of complexity required by such problems. Using an example application, namely Sea Surface Temperature Prediction, we show how general background knowledge gained from physics could be used as a guideline for designing efficient Deep Learning models. In order to motivate the approach and to assess its generality we demonstrate a formal link between the solution of a class of differential equations underlying a large family of physical phenomena and the proposed model. Experiments and comparison with series of baselines including a state of the art numerical approach is then provided.

Key facts. Cited by 95 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Nov 2017.

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Citing papers per year: 2021: 25; 2022: 22; 2023: 18; 2024: 8; 2025: 13; 2026: 9.

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  2. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 105
  3. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  4. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 80
  5. 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 77
  6. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
  7. 2023On the Connection Between MPNN and Graph Transformercited by 60
  8. 2021Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modelingcited by 59
  9. 2023Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformerscited by 54
  10. 2022Generalizing to New Physical Systems via Context-Informed Dynamics Modelcited by 49
  11. 2023PastNet: Introducing Physical Inductive Biases for Spatio-temporal Video Predictioncited by 44
  12. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
38 more
  1. 2021LEADS: Learning Dynamical Systems that Generalize Across Environmentscited by 39
  2. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
  3. 2024Neural Methods for Amortized Inferencecited by 36
  4. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  5. 2022Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networkscited by 33
  6. 2022MAgNet: Mesh Agnostic Neural PDE Solvercited by 28
  7. 2021Towards a Collective Agenda on AI for Earth Science Data Analysiscited by 27
  8. 2022Differentiable Programming for Earth System Modelingcited by 21
  9. 2021Climate Modeling with Neural Diffusion Equationscited by 20
  10. 2025Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networkscited by 19
  11. 2021Physically Explainable CNN for SAR Image Classificationcited by 16
  12. 2021Bridging observation, theory and numerical simulation of the ocean using Machine Learningcited by 15
  13. 2022Statistical Deep Learning for Spatial and Spatio-Temporal Datacited by 15
  14. 2025Deep Learning and Foundation Models for Weather Prediction: A Surveycited by 15
  15. 2022Filtered-CoPhy: Unsupervised Learning of Counterfactual Physics in Pixel Spacecited by 14
  16. 2023A Hierarchical Spatial Transformer for Massive Point Samples in Continuous Spacecited by 10
  17. 2021Deep KKL: Data-driven Output Prediction for Non-Linear Systemscited by 9
  18. 2024Modeling Spatio-temporal Dynamical Systems with Neural Discrete Learning and Levels-of-Expertscited by 9
  19. 2023Bayesian neural networks via MCMC: a Python-based tutorialcited by 8
  20. 2025Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Modelscited by 8
  21. 2025The wall confronting large language modelscited by 8
  22. 2026Test-time Generalization for Physics through Neural Operator Splittingcited by 8
  23. 2021Physics-informed generative neural network: an application to troposphere temperature predictioncited by 7
  24. 2021A spatio-temporal LSTM model to forecast across multiple temporal and spatial scalescited by 6
  25. 2024Space and Time Continuous Physics Simulation From Partial Observationscited by 6
  26. 2023Exploring Effective Priors and Efficient Models for Weakly-Supervised Change Detectioncited by 5
  27. 2021Learning Runge-Kutta Integration Schemes for ODE Simulation and Identificationcited by 4
  28. 2021Physics-Aware Downsampling with Deep Learning for Scalable Flood Modelingcited by 4
  29. 2021Deep Decomposition for Stochastic Normal-Abnormal Transportcited by 4
  30. 2022Learning to Estimate and Refine Fluid Motion with Physical Dynamicscited by 4
  31. 2022Efficient data-driven gap filling of satellite image time series using deep neural networks with partial convolutionscited by 4
  32. 2022Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilationcited by 4
  33. 2022Learning Modular Simulations for Homogeneous Systemscited by 4
  34. 2025Unraveling Normal Anatomy via Fluid-Driven Anomaly Randomizationcited by 4
  35. 2025Improving Long-term Autoregressive Spatiotemporal Predictions: A Proof of Concept with Fluid Dynamicscited by 4
  36. 2022A Model-Constrained Tangent Slope Learning Approach for Dynamical Systemscited by 3
  37. 2022Learning 4DVAR inversion directly from observationscited by 3
  38. 2023Inductive biases in deep learning models for weather predictioncited by 3

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