A Stochastic Locally Diffusive Model with Neural Network-Based Deformations for Global Sea Surface Temperature

Abstract

In this work, we propose a new approach to model large, irregularly distributed spatio-temporal global data via a locally diffusive stochastic partial differential equation (SPDE). The proposed model assumes a local deformation of the SPDE with non-linear dependence on the covariates through a neural network. The proposed model can be fit in a computationally efficient manner using a triangulation over the sphere and sparsity of the precision matrix, as shown in an application with a large data set of simulated multi-decadal monthly sea surface temperature.