Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation law

TL;DR

This paper introduces the Hamiltonian Neural Koopman Operator (HNKO), a physics-informed machine learning approach that accurately models and discovers conservation laws in complex dynamical systems, even with noisy data.

Contribution

The paper proposes HNKO, integrating physics knowledge into Koopman operator learning to automatically preserve and discover conservation laws in Hamiltonian systems.

Findings

HNKO outperforms existing methods on various physical systems.

It effectively handles systems with hundreds or thousands of degrees of freedom.

The approach reinforces machine learning's capability in solving physical problems.

Abstract

Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural Koopman Operator (HNKO), integrating the knowledge of mathematical physics in learning the Koopman operator, and making it automatically sustain and even discover the conservation laws. We demonstrate the outperformance of the HNKO and its extension using a number of representative physical systems even with hundreds or thousands of freedoms. Our results suggest that feeding the prior knowledge of the underlying system and the mathematical theory appropriately to the learning framework can reinforce the capability of machine learning in solving physical problems.