System identification using Bayesian neural networks with nonparametric noise models
This work addresses system identification for science and engineering applications, offering a more flexible method for modeling noise and uncertainty, though it appears incremental by building on existing Bayesian and neural network techniques.
The authors tackled the problem of system identification in stochastic dynamic systems by proposing a Bayesian nonparametric approach that estimates system parameters and unknown noise processes using flexible probability density functions and Bayesian neural networks, demonstrating effectiveness on simulated and real time series.
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.