Learning Hamiltonian Dynamics with Bayesian Data Assimilation

2025-01-31

AI Summary

To address long-term trajectory prediction for unknown Hamiltonian systems, this paper proposes a neural surrogate modeling framework that jointly incorporates physical conservation laws and data adaptability. Methodologically, we introduce an autoregressive Hamiltonian neural network that jointly models generalized coordinates and conjugate momenta; crucially, we integrate variational Bayesian filtering with online data assimilation into the autoregressive training pipeline, enabling real-time error correction under strict energy conservation constraints. Our key contribution lies in unifying physics-informed priors—specifically, the intrinsic Hamiltonian structure—with Bayesian uncertainty quantification, thereby achieving both long-term numerical stability and rapid adaptation to observations. Evaluated on strongly perturbed elliptical orbits and multi-degree-of-freedom spring-mass systems, our method reduces energy error by over one order of magnitude and significantly outperforms state-of-the-art approaches in long-horizon prediction accuracy and robustness.

Technology Category

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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.

Problem

• Complex Physical Systems
• Hamiltonian Rule
• Motion Prediction

Innovation

• Bayesian data fusion
• Hamiltonian rule
• Neural network design