Physically Informed Neural Networks for the Simulation and Data-Assimilation of Geophysical Dynamics

The forecasting and assimilation of sea surface dynamics from satellite-derived data is a challenging issue. Data-driven approaches have arisen as promising schemes to fully exploit satellite observations. A key feature of sea surface dynamics is that they relate to partially-observed dynamics. Here, guided by physical and mathematical considerations of the underlying dynamics of a given system, we propose a novel neural networks architecture for the identification of ordinary differential equations (ODE) of partially observed systems. Numerical experiments for toy models and a sea level anomaly dynamics illustrate the relevance of the proposed scheme for forecasting and assimilation issues w.r.t. other state-of-the-art data-driven models.