System identification using Bayesian neural networks with nonparametric noise models

TL;DR

This paper introduces a Bayesian nonparametric framework using neural networks for system identification in stochastic nonlinear systems, allowing flexible noise modeling and uncertainty quantification.

Contribution

It develops a novel Bayesian neural network approach with nonparametric noise models for improved system identification in nonlinear stochastic systems.

Findings

Effective on simulated data

Demonstrated on real time series

Flexible noise modeling achieved

Abstract

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along with its unknown noise processes. In particular, we propose a Bayesian nonparametric approach for system identification in discrete time nonlinear random dynamical systems assuming only the order of the Markov process is known. The proposed method replaces the assumption of Gaussian distributed error components with a highly flexible family of probability density functions based on Bayesian nonparametric priors. Additionally, the functional form of the system is estimated by leveraging Bayesian neural networks which also leads to flexible uncertainty quantification. Asymptotically on the number of hidden neurons, the proposed model converges to full nonparametric Bayesian regression model. A Gibbs sampler for posterior inference is proposed and its effectiveness is illustrated on simulated and real time series.