Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation law
This addresses the problem of noisy dynamics prediction for researchers in physics and machine learning, though it appears incremental as it builds on existing Koopman operator methods.
The authors tackled the challenge of accurately predicting dynamics from noisy observational data in Hamiltonian systems by proposing the Hamiltonian Neural Koopman Operator (HNKO), which integrates mathematical physics knowledge to automatically sustain and discover conservation laws. They demonstrated its outperformance on representative physical systems with hundreds or thousands of degrees of freedom.
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.