mlsanityData to 14 Oct 2026

Governing Equation Discovery from Data Based on Differential Invariants

arXiv 2505.18798 ↗First posted 24 May 2025cs.LG stat.MLcited by 4

Not on the map. Why?

Abstract (arXiv)

The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs) from data poses significant challenges, primarily in determining relevant terms from a vast search space. Symmetry, as a crucial prior knowledge in scientific fields, has been widely applied in tasks such as designing equivariant networks and guiding neural PDE solvers. In this paper, we propose a pipeline for governing equation discovery based on differential invariants, which can losslessly reduce the search space of existing equation discovery methods while strictly adhering to symmetry. Specifically, we compute the set of differential invariants corresponding to the infinitesimal generators of the symmetry group and select them as the relevant terms for equation discovery. Taking DI-SINDy (SINDy based on Differential Invariants) as an example, we demonstrate that its success rate and accuracy in PDE discovery surpass those of other symmetry-informed governing equation discovery methods across a series of PDEs.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 39 of its 59 references that are in the map. First posted on arXiv 24 May 2025.

Builds on

39 of 59 references.

References · 39

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2017Deep Setscited by 1,421
  3. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  4. 2019Hamiltonian Neural Networkscited by 712
  5. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
  6. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
  7. 2022Message Passing Neural PDE Solverscited by 386
  8. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  9. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 344
  10. 2019Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradientscited by 309
  11. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
  12. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 216
27 more
  1. 2021Contemporary Symbolic Regression Methods and their Relative Performancecited by 215
  2. 2022End-to-end symbolic regression with transformerscited by 203
  3. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  4. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 194
  5. 2021Neural Symbolic Regression that Scalescited by 192
  6. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  7. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 126
  8. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 83
  9. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 77
  10. 2021Physics-based Deep Learningcited by 68
  11. 2022Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree searchcited by 66
  12. 2023Clifford Group Equivariant Neural Networkscited by 55
  13. 2019Learning Symbolic Physics with Graph Networkscited by 53
  14. 2023Generative Adversarial Symmetry Discoverycited by 42
  15. 2023Learning Neural PDE Solvers with Parameter-Guided Channel Attentioncited by 38
  16. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 38
  17. 2022LieGG: Studying Learned Lie Group Generatorscited by 31
  18. 2023Latent Space Symmetry Discoverycited by 29
  19. 2023Lie Point Symmetry and Physics Informed Networkscited by 24
  20. 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 24
  21. 2024Active Learning for Neural PDE Solverscited by 22
  22. 2024Learning Infinitesimal Generators of Continuous Symmetries from Datacited by 17
  23. 2024Symmetry-Informed Governing Equation Discoverycited by 15
  24. 2024Symmetry Discovery Beyond Affine Transformationscited by 15
  25. 2022Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equationscited by 11
  26. 2022Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equationscited by 5
  27. 2025Generalized Lie Symmetries in Physics-Informed Neural Operatorscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Adaptive Symmetry Discovery for Dynamical System Identificationcited by 3
  2. 2026Efficient Learning and Symmetry Discovery under Exact Invariancescited by 3
  3. 2026EqOD: Symmetry-Informed Stability Selection for PDE Identificationcited by 0
  4. 2026LieDiscover: Adaptive Symbolic Library Construction for Explicit Open-form Symmetry Discoverycited by 0