System identification using Bayesian neural networks with nonparametric noise models

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 estimating 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 in simulated and real time series.

Sensitivity-Guided Iterative Parameter Identification and Data Generation with BayesFlow and PELS-VAE for Model Calibration

“…An ensemble learning method integrating stochastic components into neural networks, the Bayesian Neural Network (BNN) [2] has been proved to fulfill high accuracy and more robustness in out-of-distribution samples [3]. Furthermore, BNNs enable better identification of stochastic dynamical systems [4]. Another expressive probabilistic modeling and inference method, Normalizing Flow [5] equipped with structural invertibility [6] has been deeply explored and widely applied, as summarized in [7,8].…”