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