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

TL;DR

This paper introduces a bilinear residual neural network architecture for modeling and forecasting dynamical systems, leveraging data-driven approaches to improve upon traditional differential equation models.

Contribution

It proposes a novel neural network architecture with bilinear layers, reinterpreting Runge-Kutta methods as graphical models for better system identification and forecasting.

Findings

Enhanced forecasting accuracy on classic dynamical systems

Effective system identification using the proposed neural network

Demonstrated relevance of bilinear residual networks in numerical experiments

Abstract

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.