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Physics-based Deep Learning

arXiv 2109.05237 ↗First posted 11 Sep 2021cs.LG physics.comp-phcited by 67

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Abstract (arXiv)

This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up and running quickly. Beyond traditional supervised learning, we dive into physical loss-constraints, differentiable simulations, diffusion-based approaches for probabilistic generative AI, as well as reinforcement learning and advanced neural network architectures. These foundations are paving the way for the next generation of scientific foundation models. We are living in an era of rapid transformation. These methods have the potential to redefine what's possible in computational science.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Sep 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 17; 2023: 13; 2024: 15; 2025: 12; 2026: 8.

67 papers.

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  1. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 205
  2. 2022Clifford Neural Layers for PDE Modelingcited by 91
  3. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  4. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
  5. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 76
  6. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 65
  7. 2025AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformerscited by 49
  8. 2022Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizonscited by 39
  9. 2022A posteriori learning for quasi-geostrophic turbulence parametrizationcited by 36
  10. 2024Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modelingcited by 36
  11. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  12. 2022DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualizationcited by 32
38 more
  1. 2025PDE-Transformer: Efficient and Versatile Transformers for Physics Simulationscited by 29
  2. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 25
  3. 2022EINNs: Epidemiologically-informed Neural Networkscited by 21
  4. 2022Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustrationcited by 21
  5. 2023Solving Inverse Physics Problems with Score Matchingcited by 15
  6. 2024Diffeomorphism Neural Operator for various domains and parameters of partial differential equationscited by 15
  7. 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
  8. 2023A Multifidelity deep operator network approach to closure for multiscale systemscited by 11
  9. 2024Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamicscited by 10
  10. 2024Metamizer: a versatile neural optimizer for fast and accurate physics simulationscited by 7
  11. 2025Physics-Driven Learning for Inverse Problems in Quantum Chromodynamicscited by 7
  12. 2025GyroSwin: 5D Surrogates for Gyrokinetic Plasma Turbulence Simulationscited by 7
  13. 2022Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equationscited by 5
  14. 2022Selected Trends in Artificial Intelligence for Space Applicationscited by 5
  15. 2025Governing Equation Discovery from Data Based on Differential Invariantscited by 4
  16. 2023Inductive biases in deep learning models for weather predictioncited by 3
  17. 2023Extreme heatwave sampling and prediction with analog Markov chain and comparisons with deep learningcited by 3
  18. 2023Improved prediction of ligand-protein binding affinities by meta-modelingcited by 3
  19. 2024JAX-SPH: A Differentiable Smoothed Particle Hydrodynamics Frameworkcited by 3
  20. 2024Stabilizing Backpropagation Through Time to Learn Complex Physicscited by 3
  21. 2025PRDP: Progressively Refined Differentiable Physicscited by 3
  22. 2022DeepClouds.ai: Deep learning enabled computationally cheap direct numerical simulationscited by 2
  23. 2024Accelerating Legacy Numerical Solvers by Non-intrusive Gradient-based Meta-solvingcited by 2
  24. 2024Combining Federated Learning and Control: A Surveycited by 2
  25. 2021Does Explainable Machine Learning Uncover the Black Box in Vision Applications?cited by 1
  26. 2022Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNscited by 1
  27. 2022FO-PINNs: A First-Order formulation for Physics Informed Neural Networkscited by 1
  28. 2022Exploring Physical Latent Spaces for High-Resolution Flow Restorationcited by 1
  29. 2023Deep learning modelling of manufacturing and build variations on multi-stage axial compressors aerodynamicscited by 1
  30. 2024Modern, Efficient, and Differentiable Transport Equation Models using JAX: Applications to Population Balance Equationscited by 1
  31. 2025PhysicsGen: Can Generative Models Learn from Images to Predict Complex Physical Relations?cited by 1
  32. 2025Towards scientific machine learning for granular material simulations -- challenges and opportunitiescited by 1
  33. 2025Leveraging Analytic Gradients in Provably Safe Reinforcement Learningcited by 1
  34. 2025Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulationscited by 1
  35. 2026Adjoint-based shape optimization of a ship hull using a Conditional Variational Autoencoder (CVAE) assisted propulsion surrogate modelcited by 1
  36. 2026From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontiercited by 1
  37. 2022Differentiable Physics-based Greenhouse Simulationcited by 0
  38. 2022Differentiable optimization of the Debye-Wolf integral for light shaping and adaptive optics in two-photon microscopycited by 0

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