Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Models

TL;DR

This paper introduces a Bayesian approach for identifying and estimating nonseparable Hamiltonian systems from noisy, sparse data, achieving higher accuracy and robustness than existing methods.

Contribution

It presents a novel probabilistic Bayesian framework specifically designed for nonseparable Hamiltonian systems, improving prediction accuracy and uncertainty quantification.

Findings

Achieves less than 10% relative error over extended prediction periods

Outperforms state-of-the-art methods in accuracy and uncertainty reduction

Demonstrates robustness with sparse and noisy measurements

Abstract

This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse science and engineering applications such as astrophysics, robotics, vortex dynamics, charged particle dynamics, and quantum mechanics. The numerical experiments demonstrate that the proposed method recovers dynamical systems with higher accuracy and reduced predictive uncertainty compared to state-of-the-art approaches. The results further show that accurate predictions far outside the training time interval in the presence of sparse and noisy measurements are possible, which lends robustness and generalizability to the proposed approach. A quantitative benefit is prediction accuracy with less than 10% relative error for more than 12 times longer than a comparable least-squares-based method on a benchmark problem.