Learning the Spatio-Temporal Dynamics of Physical Processes from Partial Observations

Ibrahim Ayed, Emmanuel de Bézenac, Arthur Pajot, patrick gallinari

Abstract: We consider the problem of automatically learning the dynamics of physical processes evolving in space and time from incomplete observations. This is a central problem in many fields that remains complicated for large observation spaces and complex dynamics. We propose a data-driven framework, where the system's dynamics are modeled by an unknown time-varying differential equation and the evolution term for the state is estimated from the partially observed data only, using a deep convolutional neural network. Our method yields improvements w.r.t. state-of-the-art recurrent deep network models for the forecast of observations corresponding to complex fluid dynamics. We analyze the latent state representations learned by this model and propose two settings that help interpret the learned states. The model is evaluated on the incompressible Navier Stokes equations.