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.
@article{arxiv.1712.07003,
title = {Bilinear residual Neural Network for the identification and forecasting of dynamical systems},
author = {Ronan Fablet and Said Ouala and Cedric Herzet},
journal= {arXiv preprint arXiv:1712.07003},
year = {2017}
}