# Symmetry-Informed Governing Equation Discovery

arXiv: https://arxiv.org/abs/2405.16756 · HTML: https://mlsanity.com/paper/2405.16756/

## 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 (most cited first, 23 of 23)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Automatic Symmetry Discovery with Lie Algebra Convolutional Network](https://mlsanity.com/paper/2109.07103/) (2021)
- [Lie Point Symmetry Data Augmentation for Neural PDE Solvers](https://mlsanity.com/paper/2202.07643/) (2022)
- [Learning Symbolic Physics with Graph Networks](https://mlsanity.com/paper/1909.05862/) (2019)
- [Generative Adversarial Symmetry Discovery](https://mlsanity.com/paper/2302.00236/) (2023)
- [Machine-learning hidden symmetries](https://mlsanity.com/paper/2109.09721/) (2021)
- [Self-Supervised Learning with Lie Symmetries for Partial Differential Equations](https://mlsanity.com/paper/2307.05432/) (2023)
- [Latent Space Symmetry Discovery](https://mlsanity.com/paper/2310.00105/) (2023)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [Lie Point Symmetry and Physics Informed Networks](https://mlsanity.com/paper/2311.04293/) (2023)
- [Learning Layer-wise Equivariances Automatically using Gradients](https://mlsanity.com/paper/2310.06131/) (2023)
- [Dimensionally Consistent Learning with Buckingham Pi](https://mlsanity.com/paper/2202.04643/) (2022)
- [Time-Reversal Symmetric ODE Network](https://mlsanity.com/paper/2007.11362/) (2020)
- [Learning ODE Models with Qualitative Structure Using Gaussian Processes](https://mlsanity.com/paper/2011.05364/) (2020)
- [Physics-informed dynamic mode decomposition (piDMD)](https://mlsanity.com/paper/2112.04307/) (2021)

## Built on by (most cited first, 15 of 15)

- [Think like a Scientist: Physics-guided LLM Agent for Equation Discovery](https://mlsanity.com/paper/2602.12259/) (2026)
- [Towards autonomous quantum physics research using LLM agents with access to intelligent tools](https://mlsanity.com/paper/2511.11752/) (2025)
- [Discovering Symbolic Differential Equations with Symmetry Invariants](https://mlsanity.com/paper/2505.12083/) (2025)
- [Explicit Discovery of Nonlinear Symmetries from Dynamic Data](https://mlsanity.com/paper/2510.01855/) (2025)
- [Latent Mixture of Symmetries for Sample-Efficient Dynamic Learning](https://mlsanity.com/paper/2510.03578/) (2025)
- [Governing Equation Discovery from Data Based on Differential Invariants](https://mlsanity.com/paper/2505.18798/) (2025)
- [Scaling Laws and Symmetry, Evidence from Neural Force Fields](https://mlsanity.com/paper/2510.09768/) (2025)
- [Adaptive Symmetry Discovery for Dynamical System Identification](https://mlsanity.com/paper/2608.08091/) (2026)
- [Efficient Learning and Symmetry Discovery under Exact Invariances](https://mlsanity.com/paper/2609.07031/) (2026)
- [Physics-informed reduced-order modelling with equivariant spectral submanifolds](https://mlsanity.com/paper/2608.04239/) (2026)
- [LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries](https://mlsanity.com/paper/2510.25731/) (2025)
- [Fast and principled equation discovery from chaos to climate](https://mlsanity.com/paper/2604.11929/) (2026)
- [EqOD: Symmetry-Informed Stability Selection for PDE Identification](https://mlsanity.com/paper/2605.11524/) (2026)
- [On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement](https://mlsanity.com/paper/2607.23753/) (2026)
- [Discovering Physical Representation Languages](https://mlsanity.com/paper/2609.23381/) (2026)

## 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.