Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes

In this paper, we propose a Gaussian process-based nonlinear, time-varying drift model for stochastic differential equations. In particular, we combine eigenfunction expansion of the Gaussian process’ covariance kernel in the spatial input variables with spectral decomposition in the time domain to obtain a reduced rank state space representation of the drift model, which avoids the growing complexity (with respect to time) of the full Gaussian process solution. The proposed approach is evaluated on two nonlinear benchmark problems, the Bouc Wen and the cascaded tanks systems.