Data-driven Stein variational method for precise estimation of nonlinear dynamical system

Abstract

Accurate estimation of latent nonlinear dynamical systems from time-series data is essential for understanding complex systems. We propose a data-driven method for precise state and parameter estimation using Stein variational gradient descent (SVGD) method combined with the expectation-maximization (EM) algorithm. Unlike conventional Bayesian filtering, which suffers from weight degeneracy and multidimensional challenges, our approach maintains particle diversity and accurately represents the posterior distribution. Our experiments demonstrate that the proposed method achieves high accuracy in latent variable and parameter estimation. The results underscore the method's effectiveness in handling multidimensional and nonlinear systems, making it a valuable tool for dynamic system modeling.