LieDiscover: Adaptive Symbolic Library Construction for Explicit Open-form Symmetry Discovery

arXiv:2609.33663 · cs.SC, cs.LG · Submitted 2026-09-27 · Read on arXiv

cs.SC, cs.LG

Submitted: 2026-09-27

Updated: 2026-09-27

Terminology

• Pruning — 18× in this paper · explained in 4 episodes
• Actor — 10× in this paper · explained in 3 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Data Augmentation — 7× in this paper · explained in 7 episodes
• Reinforcement Learning — 4× in this paper · explained in 4 episodes
• Symbolic Regression — 4× in this paper · explained in 5 episodes
• Singular Value Decomposition — 3× in this paper
• Adversarial Training — 2× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Latent Space — 2× in this paper · explained in 7 episodes
• Linearized Alternating Direction Method with Adaptive Penalty — 2× in this paper
• Regularization — 2× in this paper · explained in 3 episodes
• Spectral Gap — 2× in this paper · explained in 5 episodes
• Action Space — 1× in this paper · explained in 1 episode
• Admissibility — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Fourier Neural Operator — 1× in this paper
• LieDiscover for Lie Point Symmetry Data Augmentation — 1× in this paper
• Markov Decision Process — 1× in this paper
• Markov Decision Process (MDP) — 1× in this paper · explained in 11 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Reward Function — 1× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
• DISCOVER: Deep identification of symbolically concise open-form PDEs via enhanced reinforcement-learning
• Explicit Discovery of Nonlinear Symmetries from Dynamic Data
• Governing Equation Discovery from Data Based on Differential Invariants
• Fourier Neural Operator for Parametric Partial Differential Equations
• Extrapolation and learning equations
• Analytic solutions for the Burgers equation with source terms
• Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients
• EPOpt: Learning Robust Neural Network Policies Using Model Ensembles
• Optimizing the CVaR via Sampling
• Discovering Symbolic Differential Equations with Symmetry Invariants
• Latent Space Symmetry Discovery
• Meta-Learning Symmetries by Reparameterization

Related papers

• Simple generators of rational function fields
• Resultant Tools for Parametric Polynomial Systems with Application to Mathematical Biology
• Generic Characteristic-Zero Equivalence Between Derivative B'ezout Inversion and Multipoint Evaluation
• Diversity of EML-type operators
• Physical Law Ecology: mapping multi-mechanism ecologies as the zeroth step of data-driven scientific discovery
• Learning Fast Monomial Orders for Gr"obner Basis Computations