Bilinear Residual Neural Network for the Identification and Forecasting of Geophysical Dynamics

Due to the increasing availability of large-scale observations and simulation datasets, data-driven representations arise as efficient and relevant computation representations of geophysical systems for a wide range of applications, where model-driven models based on ordinary differential equations remain the state-of-the-art approaches. In this work, we investigate neural networks (NN) as physically-sound data-driven representations of such systems. Viewing Runge-Kutta methods as graphical models, we consider a residual NN architecture and introduce bilinear layers to embed non-linearities which are intrinsic features of geophysical systems. From numerical experiments for synthetic and real datasets, we demonstrate the relevance of the proposed NN-based architecture both in terms of forecasting performance and model identification.