Learning Hamiltonian Dynamics with Bayesian Data Assimilation
This work addresses the challenge of long-term prediction in Hamiltonian systems, which is important for fields like physics and engineering, but it appears incremental as it builds on existing neural network methods with specific enhancements.
The paper tackles the problem of time-series prediction in unknown Hamiltonian dynamical systems by developing a neural network-based approach that preserves a constant Hamiltonian and incorporates autoregressive prediction errors and Bayesian data assimilation. The result is demonstrated through numerical experiments on a spring-mass system and highly elliptic orbits, showing effectiveness for accurate and robust long-term predictions.
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.