Uncertainty quantification in neural state-space models: Applications for experiment design and uncertainty-aware MPC

Abstract

This paper addresses the problem of uncertainty quantification in neural state-space models from a Bayesian perspective. The posterior distribution over the neural network parameters is derived and approximated using the Laplace method, resulting in a Gaussian approximation of the model’s predictive distribution. Based on the predictive distribution, we introduce an uncertainty index that quantifies the model’s confidence over any possible input sequence, enabling the detection of out-of-distribution regimes. This index is then leveraged in two applications: (i) experiment design for the identification of state-space models, and (ii) model predictive control under epistemic uncertainty.