Automated Discovery of Conservation Laws via Hybrid Neural ODE-Transformers
This work addresses the challenge of identifying conservation laws from observational data, which is incremental as it builds on existing methods with a novel hybrid approach.
The authors tackled the problem of automating the discovery of conservation laws from noisy trajectory data by proposing a hybrid framework integrating Neural ODEs, Transformers, and a symbolic-numeric verifier, and showed that it significantly outperforms baselines on canonical physical systems.
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.