Deep Variational System Identification for Nonlinear State-Space Models via Alternating Optimization

Abstract

Nonlinear state-space model identification is inherently challenging due to the need for joint latent-state inference and parameter learning. Variational inference offers a tractable framework, where structured Gaussian posteriors enable scalable inference over latent trajectories. However, existing parameterizations of the posterior mean struggle to capture complex nonlinear dynamics, while more expressive deep parameterizations tend to introduce instability in joint optimization. To address these issues, this article proposes a deep variational identification method for nonlinear state-space models based on a structured Gaussian posterior. Specifically, the posterior mean is parameterized using a non-causal dilated residual convolutional network, while a Markov structure with block-tridiagonal precision is preserved to ensure linear-time inference. Furthermore, an alternating optimization scheme is developed to separate variational smoothing from model identification. The variational parameters are updated by maximizing a differentiable approximation to the evidence lower bound, whereas the model and noise parameters are updated via analytic identification steps using samples from the variational posterior. Experiments on a nonlinear discrete-time system and a stochastic Duffing oscillator demonstrate that the proposed approach achieves stable optimization and reliable estimation of the system dynamics and noise statistics.