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Due to the increasing availability of large-scale observation and simulationdatasets, data-driven representations arise as efficient and relevantcomputation representations of dynamical systems for a wide range ofapplications, where model-driven models based on ordinary differential equationremain the state-of-the-art approaches. In this work, we investigate neuralnetworks (NN) as physically-sound data-driven representations of such systems.Reinterpreting Runge-Kutta methods as graphical models, we consider a residualNN architecture and introduce bilinear layers to embed non-linearities whichare intrinsic features of dynamical systems. From numerical experiments forclassic dynamical systems, we demonstrate the relevance of the proposedNN-based architecture both in terms of forecasting performance and modelidentification.

Bilinear residual Neural Network for the identification and forecasting of dynamical systems