Automated Discovery of Conservation Laws via Hybrid Neural ODE-Transformers

TL;DR

This paper introduces a hybrid neural ODE-Transformer framework that automates the discovery of conservation laws from noisy observational data, combining continuous modeling, symbolic candidate generation, and numerical verification.

Contribution

It presents a novel integrated approach that automates invariant discovery using Neural ODEs, Transformers, and symbolic-numeric verification, outperforming existing methods.

Findings

Outperforms baseline methods on physical systems

Robustly discovers conservation laws from noisy data

Demonstrates effectiveness of decoupled learn-then-search approach

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.