Automated Discovery of Conservation Laws via Hybrid Neural ODE-Transformers

Vivan Doshi

Keywords: Neural Ordinary Differential Equations, symbolic regression, conservation laws, invariant discovery, dynamical systems, transformer models, hybrid modeling, data-driven scientific discovery, noise-robust learning, symbolic-numeric verification, equation discovery, AI for physics, machine learning for scientific discovery

TL;DR: Automates discovery of conservation laws by combining Neural ODE dynamics learning, Transformer-based symbolic generation, and rigorous numerical verification to recover invariants from noisy dynamical data.

Abstract: The discovery of conservation laws is a cornerstone of scientific progress. However, identifying these invariants from observational data remains a significant challenge. We propose a hybrid framework to automate the discovery of conserved quantities from noisy trajectory data. Our approach integrates three components: (1) a Neural Ordinary Differential Equation (Neural ODE) that learns a continuous model of the system's dynamics, (2) a Transformer that generates symbolic candidate invariants conditioned on the learned vector field, and (3) a symbolic-numeric verifier that provides a strong numerical certificate for the validity of these candidates. We test our framework on canonical physical systems and show that it significantly outperforms baselines that operate directly on trajectory data. This work demonstrates the robustness of a decoupled learn-then-search approach for discovering mathematical principles from imperfect data.

Submission Number: 205