Learning Hamiltonian Dynamics with Bayesian Data Assimilation

TL;DR

This paper presents a neural network approach for predicting Hamiltonian system dynamics, combining surrogate modeling, autoregressive training, and Bayesian data assimilation to improve long-term accuracy and robustness.

Contribution

It introduces an Autoregressive Hamiltonian Neural Network and integrates Bayesian data assimilation for real-time refinement, advancing long-term prediction in unknown Hamiltonian systems.

Findings

Effective long-term predictions demonstrated on spring-mass and orbital systems.

Autoregressive training improves prediction accuracy over time.

Bayesian data assimilation enhances robustness with real-time data.

Abstract

In this paper, we develop a neural network-based approach for time-series prediction in unknown Hamiltonian dynamical systems. Our approach leverages a surrogate model and learns the system dynamics using generalized coordinates (positions) and their conjugate momenta while preserving a constant Hamiltonian. To further enhance long-term prediction accuracy, we introduce an Autoregressive Hamiltonian Neural Network, which incorporates autoregressive prediction errors into the training objective. Additionally, we employ Bayesian data assimilation to refine predictions in real-time using online measurement data. Numerical experiments on a spring-mass system and highly elliptic orbits under gravitational perturbations demonstrate the effectiveness of the proposed method, highlighting its potential for accurate and robust long-term predictions.