Automatic-differentiated Physics-Informed Echo State Network (API-ESN)

TL;DR

The paper introduces API-ESN, a physics-informed neural network that uses automatic differentiation to significantly improve the accuracy of time-derivative calculations, enabling better reconstruction of chaotic systems.

Contribution

It presents a novel API-ESN model that enhances the accuracy of physics-informed echo state networks through automatic differentiation, especially for chaotic systems.

Findings

Accuracy of time-derivative increased by up to seven orders of magnitude.

Improved reconstruction of unmeasured states in chaotic systems.

Eliminates errors in derivative computation present in previous models.

Abstract

We propose the Automatic-differentiated Physics-Informed Echo State Network (API-ESN). The network is constrained by the physical equations through the reservoir's exact time-derivative, which is computed by automatic differentiation. As compared to the original Physics-Informed Echo State Network, the accuracy of the time-derivative is increased by up to seven orders of magnitude. This increased accuracy is key in chaotic dynamical systems, where errors grows exponentially in time. The network is showcased in the reconstruction of unmeasured (hidden) states of a chaotic system. The API-ESN eliminates a source of error, which is present in existing physics-informed echo state networks, in the computation of the time-derivative. This opens up new possibilities for an accurate reconstruction of chaotic dynamical states.