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.
@article{arxiv.2501.18808,
title = {Learning Hamiltonian Dynamics with Bayesian Data Assimilation},
author = {Taehyeun Kim and Tae-Geun Kim and Anouck Girard and Ilya Kolmanovsky},
journal= {arXiv preprint arXiv:2501.18808},
year = {2025}
}