Modelling spatiotemporal dynamics from Earth observation data with neural differential equations

Abstract

Forecasting complex spatiotemporal dynamics is central in Earth science for modeling a variety of phenomena ranging from atmospheric dynamics to the evolution of vegetation. Those phenomena are often observed from remote sensing measurements that only provide partial information on the underlying physical equations. In this context, we consider the problem of automatically learning the dynamics of physical spatiotemporal processes from incomplete observations. We propose a new data-driven framework where the dynamics is modeled by an unknown differential equation and where the state representation and evolution is learned only from partial observations. The dynamical model is parametrized by a deep neural network. Since the problem is underconstrained, the model may learn high quality forecasts of the observations while being physically inconsistent. We introduce two settings that help analyze and interpret the learned model states. We evaluate the proposed model on two benchmarks: (1) the incompressible Navier–Stokes equations which underlie transport phenomena in the atmosphere and in the ocean, (2) a challenging problem of sea surface temperature prediction where the underlying dynamics corresponds to a sophisticated ocean dynamics model. The proposed model is able to provide long term forecasts for these complex dynamics and large dimensional observation spaces.