# Learning Hamiltonian Dynamics with Bayesian Data Assimilation

arXiv: https://arxiv.org/abs/2501.18808 · HTML: https://mlsanity.com/paper/2501.18808/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2025.

## Abstract (arXiv)

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.