Learning unseen coexisting attractors

TL;DR

This paper demonstrates that next-generation reservoir computing effectively learns complex dynamical systems with multiple attractors, requiring less data and training time, and achieving higher accuracy than traditional methods.

Contribution

It provides a comparative analysis showing the superior performance of next-generation reservoir computing in learning systems with multiple coexisting attractors.

Findings

Next-generation reservoir computing uses 1.7x less training data.

It requires 1000x shorter warm-up time.

It achieves 100x higher accuracy in predicting attractor characteristics.

Abstract

Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing approaches. Recently, a simpler formulation, known as next-generation reservoir computing, removes many algorithm metaparameters and identifies a well-performing traditional reservoir computer, thus simplifying training even further. Here, we study a particularly challenging problem of learning a dynamical system that has both disparate time scales and multiple co-existing dynamical states (attractors). We compare the next-generation and traditional reservoir computer using metrics quantifying the geometry of the ground-truth and forecasted attractors. For the studied four-dimensional system, the next-generation reservoir computing approach uses $\sim 1.7 \times$ less training data, requires $10^3 \times$ shorter `warm up' time, has fewer metaparameters, and has an $\sim 100\times$ higher accuracy in predicting the co-existing attractor characteristics in comparison to a traditional reservoir computer. Furthermore, we demonstrate that it predicts the basin of attraction with high accuracy. This work lends further support to the superior learning ability of this new machine learning algorithm for dynamical systems.