Equilibrium Distributions and Stability Analysis of Gaussian Process State Space Models
For researchers using GP-SSMs in nonlinear dynamics, this work provides theoretical guarantees on stability and equilibrium, which are essential for safe and reliable model deployment.
This paper analyzes equilibrium distributions and stability properties of Gaussian Process State Space Models (GP-SSM), showing that with squared exponential covariance function the model is always mean square bounded and has a positive recurrent set.
Gaussian Process State Space Models (GP-SSM) are a data-driven stochastic model class suitable to represent nonlinear dynamics. They have become increasingly popular in non-parametric modeling approaches since they provide not only a prediction of the system behavior but also an accuracy of the prediction. For the application of these models, the analysis of fundamental system properties is required. In this paper, we analyze equilibrium distributions and stability properties of the GP-SSM. The computation of equilibrium distributions is based on the numerical solution of a Fredholm integral equation of the second kind and is suitable for any covariance function. Besides, we show that the GP-SSM with squared exponential covariance function is always mean square bounded and there exists a set which is positive recurrent.