mlsanityData to 14 Oct 2026

Symmetry-Informed Governing Equation Discovery

arXiv 2405.16756 ↗First posted 27 May 2024cs.LGcited by 15

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Abstract (arXiv)

Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may search an unnecessarily large space and discover less accurate or overly complex equations. In this paper, we propose to leverage symmetry in automated equation discovery to compress the equation search space and improve the accuracy and simplicity of the learned equations. Specifically, we derive equivariance constraints from the time-independent symmetries of ODEs. Depending on the types of symmetries, we develop a pipeline for incorporating symmetry constraints into various equation discovery algorithms, including sparse regression and genetic programming. In experiments across diverse dynamical systems, our approach demonstrates better robustness against noise and recovers governing equations with significantly higher probability than baselines without symmetry. Our codebase is available at https://github.com/Rose-STL-Lab/symmetry-ode-discovery.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 23 of its 43 references that are in the map. First posted on arXiv 27 May 2024.

Builds on

23 of 43 references.

References · 23

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  2. 2016Group Equivariant Convolutional Networkscited by 1,165
  3. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
  4. 2019General E(2)-Equivariant Steerable CNNscited by 446
  5. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 344
  6. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  7. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  8. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 126
  9. 2022Equivariance with Learned Canonicalization Functionscited by 109
  10. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 83
  11. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 77
  12. 2019Learning Symbolic Physics with Graph Networkscited by 53
11 more
  1. 2023Generative Adversarial Symmetry Discoverycited by 42
  2. 2021Machine-learning hidden symmetriescited by 31
  3. 2023Self-Supervised Learning with Lie Symmetries for Partial Differential Equationscited by 29
  4. 2023Latent Space Symmetry Discoverycited by 29
  5. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  6. 2023Lie Point Symmetry and Physics Informed Networkscited by 24
  7. 2023Learning Layer-wise Equivariances Automatically using Gradientscited by 23
  8. 2022Dimensionally Consistent Learning with Buckingham Picited by 22
  9. 2020Time-Reversal Symmetric ODE Networkcited by 19
  10. 2020Learning ODE Models with Qualitative Structure Using Gaussian Processescited by 9
  11. 2021Physics-informed dynamic mode decomposition (piDMD)cited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 7; 2026: 8.

15 papers.

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  1. 2026Think like a Scientist: Physics-guided LLM Agent for Equation Discoverycited by 16
  2. 2025Towards autonomous quantum physics research using LLM agents with access to intelligent toolscited by 7
  3. 2025Discovering Symbolic Differential Equations with Symmetry Invariantscited by 6
  4. 2025Explicit Discovery of Nonlinear Symmetries from Dynamic Datacited by 6
  5. 2025Latent Mixture of Symmetries for Sample-Efficient Dynamic Learningcited by 5
  6. 2025Governing Equation Discovery from Data Based on Differential Invariantscited by 4
  7. 2025Scaling Laws and Symmetry, Evidence from Neural Force Fieldscited by 4
  8. 2026Adaptive Symmetry Discovery for Dynamical System Identificationcited by 3
  9. 2026Efficient Learning and Symmetry Discovery under Exact Invariancescited by 3
  10. 2026Physics-informed reduced-order modelling with equivariant spectral submanifoldscited by 1
  11. 2025LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetriescited by 0
  12. 2026Fast and principled equation discovery from chaos to climatecited by 0
3 more
  1. 2026EqOD: Symmetry-Informed Stability Selection for PDE Identificationcited by 0
  2. 2026On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancementcited by 0
  3. 2026Discovering Physical Representation Languagescited by 0