A Nonparametric Spatio-temporal SDE Model

Cagatay Yildiz, Markus Heinonen, Harri Lähdesmäki

Abstract: We propose a nonparametric spatio-temporal stochastic differential equation (SDE) model that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We augment the input space of the drift function of an SDE with a temporal component to account for spatio-temporal patterns. The experiments on a real world data set demonstrate that the spatio-temporal model is better able to fit the data than the spatial model and also reduce the forecasting error.

Keywords: stochastic differential equation, gaussian processes, spatiotemporal drift

TL;DR: We propose a nonparametric spatio-temporal stochastic differential equation (SDE) model by augmenting the input space of the drift function of an SDE with a temporal component