mlsanityData to 14 Oct 2026

Incorporating Symmetry into Deep Dynamics Models for Improved Generalization

arXiv 2002.03061 ↗First posted 8 Feb 2020cs.LG math.RT stat.MLcited by 126

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Abstract (arXiv)

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating symmetries into convolutional neural networks. Specifically, we employ a variety of methods each tailored to enforce a different symmetry. Our models are both theoretically and experimentally robust to distributional shift by symmetry group transformations and enjoy favorable sample complexity. We demonstrate the advantage of our approach on a variety of physical dynamics including Rayleigh B'enard convection and real-world ocean currents and temperatures. Compared with image or text applications, our work is a significant step towards applying equivariant neural networks to high-dimensional systems with complex dynamics. We open-source our simulation, data, and code at urlhttps://github.com/Rose-STL-Lab/Equivariant-Net.

Key facts. Cited by 126 papers in the map (data through 14 Oct 2026). First posted on arXiv 8 Feb 2020.

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Citing papers per year: 2021: 16; 2022: 23; 2023: 28; 2024: 29; 2025: 23; 2026: 7.

126 papers.

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  1. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  2. 2021Enhancing Computational Fluid Dynamics with Machine Learningcited by 138
  3. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  4. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 97
  5. 2022Clifford Neural Layers for PDE Modelingcited by 92
  6. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 83
  7. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 77
  8. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 75
  9. 2024Equivariant Diffusion Policycited by 66
  10. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  11. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 45
  12. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 44
38 more
  1. 2023Generative Adversarial Symmetry Discoverycited by 42
  2. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 38
  3. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 38
  4. 2022Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditionscited by 33
  5. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 33
  6. 2022Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamicscited by 30
  7. 2023Self-Supervised Learning with Lie Symmetries for Partial Differential Equationscited by 29
  8. 2023Latent Space Symmetry Discoverycited by 29
  9. 2023The Exact Sample Complexity Gain from Invariances for Kernel Regressioncited by 28
  10. 2024Symmetry Considerations for Learning Task Symmetric Robot Policiescited by 28
  11. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 28
  12. 2024Zero-shot forecasting of chaotic systemscited by 28
  13. 2024Clifford-Steerable Convolutional Neural Networkscited by 25
  14. 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 24
  15. 2023Learning Layer-wise Equivariances Automatically using Gradientscited by 23
  16. 2023Machine Learning for Partial Differential Equationscited by 21
  17. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  18. 2023Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolutioncited by 20
  19. 2023A General Theory of Correct, Incorrect, and Extrinsic Equivariancecited by 19
  20. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 19
  21. 2024Equivariant Reinforcement Learning under Partial Observabilitycited by 18
  22. 2022Dimensionless machine learning: Imposing exact units equivariancecited by 17
  23. 2022Data Augmentation vs. Equivariant Networks: A Theory of Generalization on Dynamics Forecastingcited by 17
  24. 2022Set Norm and Equivariant Skip Connections: Putting the Deep in Deep Setscited by 17
  25. 2024Graph Neural PDE Solvers with Conservation and Similarity-Equivariancecited by 17
  26. 2024Learning Infinitesimal Generators of Continuous Symmetries from Datacited by 17
  27. 2024Adversarial Learning for Neural PDE Solvers with Sparse Datacited by 16
  28. 2024Symmetry-Informed Governing Equation Discoverycited by 15
  29. 2024Knowledge-guided Machine Learning: Current Trends and Future Prospectscited by 14
  30. 2021Applying Machine Learning to Study Fluid Mechanicscited by 13
  31. 2022Machine learning and invariant theorycited by 13
  32. 2024P2C2Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamicscited by 13
  33. 2021Neural Pharmacodynamic State Space Modelingcited by 12
  34. 2021Physics-constrained Deep Learning for Robust Inverse ECG Modelingcited by 12
  35. 2022Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systemscited by 12
  36. 2023Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networkscited by 12
  37. 2023On Robot Grasp Learning Using Equivariant Modelscited by 12
  38. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11

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