  Due to the increasing availability of large-scale observation and simulation
datasets, data-driven representations arise as efficient and relevant
computation representations of dynamical systems for a wide range of
applications, where model-driven models based on ordinary differential equation
remain the state-of-the-art approaches. In this work, we investigate neural
networks (NN) as physically-sound data-driven representations of such systems.
Reinterpreting 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 dynamical systems. From numerical experiments for
classic dynamical systems, we demonstrate the relevance of the proposed
NN-based architecture both in terms of forecasting performance and model
identification.
