Incorporating coupling knowledge for learning spatiotemporally chaotic dynamics

What is it about?

Machine learning methods have shown promise in learning chaotic dynamical systems, enabling model-free short-term prediction and attractor reconstruction. Our research introduces a physics-guided clustered Echo State Network (ESN) that leverages the spatial coupling structure of chaotic systems in ESN’s reservoir layer. This method outperforms existing ESN models in learning spatiotemporally chaotic dynamics, as shown by experiments on benchmark systems. More specifically, incorporating coupling knowledge into ESNs leads to a substantial reduction in computational resources, such as reservoir size and the amount of training data. We also demonstrate that incorporating this physical knowledge improves the ESN's robustness to varying learning conditions. Our approach remains effective even when the coupling knowledge is slightly imperfect or extracted directly from time series data.

Featured Image

Photo by Markus Winkler on Unsplash

Photo by Markus Winkler on Unsplash

Why is it important?

Understanding the dynamics of chaotic systems is crucial for both practical applications and theoretical analysis in science and technology. Data-driven methods are crucial for understanding chaotic systems where governing equations are unknown, such as in brain activity and social networks. While machine learning is a powerful tool for this, purely data-driven approaches can be inefficient for complex, high-dimensional systems. Physics-informed machine learning, which integrates physical knowledge into the learning process, offers a promising direction. In this work, the physical knowledge we used is the coupling structure of the underlying dynamical system, which is priorly known or extracted from data.

Perspectives