Physics-Informed Echo State Networks

TL;DR

This paper introduces a physics-informed Echo State Network that incorporates physical laws into training, enhancing the prediction of chaotic systems without extra data and improving forecast accuracy and robustness.

Contribution

The paper presents a novel physics-informed ESN that integrates governing equations into training, improving chaotic system predictions without additional data.

Findings

Enhanced predictability horizon by about two Lyapunov times.

Robustness to noise in chaotic system predictions.

Effective on Lorenz and Charney-DeVore systems.

Abstract

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training, which is based on the system's governing equations. The additional loss function penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system and a truncation of the Charney-DeVore system. Compared to the conventional ESNs, the physics-informed ESNs improve the predictability horizon by about two Lyapunov times. This approach is also shown to be robust with regard to noise. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.