2025/10/30 by Vivan Doshi, Doshi, Vivan · 1 citation
Computer Science · Materials Science · Physics and Astronomy · #Artificial neural network #Certificate #Conservation law #Generative Adversarial Networks and Image Synthesis #Hybrid system #Imperfect #Machine Learning in Materials Science #Model Reduction and Neural Networks #Robustness (evolution) #Trajectory
paper · pdf · doi:10.48550/arxiv.2511.00102
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/10/30 · openalex created_date 2025/11/05 · openalex updated_date 2026/08/05
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.