Bilinear residual Neural Network for the identification and forecasting of dynamical systems
This work addresses the need for efficient data-driven representations in dynamical systems modeling, offering a physically-sound neural network approach that is incremental in nature.
The authors tackled the problem of data-driven modeling of dynamical systems by proposing a bilinear residual neural network architecture, demonstrating improved forecasting performance and model identification in numerical experiments on classic dynamical systems.
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.