Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Models
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modeling
This paper presents a structure-preserving Bayesian approach for learning nonseparable Hamiltonian systems using stochastic dynamic models allowing for statistically-dependent, vector-valued additive and multiplicative m…
parameter estimationNonseparable Symplectic Neural Networks
Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems w…
PositionRevisiting the Effects of Stochasticity for Hamiltonian Samplers
We revisit the theoretical properties of Hamiltonian stochastic differential equations (SDES) for Bayesian posterior sampling, and we study the two types of errors that arise from numerical SDE simulation: the discretiza…
Numerical IntegrationStochastic Gradient Hamiltonian Monte Carlo with Variance Reduction for Bayesian Inference
Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stocha…
Bayesian InferenceIdentification of Nonseparable Models with Endogenous Control Variables
We study identification of the treatment effects in a class of nonseparable models with the presence of potentially endogenous control variables. We show that given the treatment variable and the controls are measurably …