Learning unseen coexisting attractors

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 ∼ 1.7× less training data, requires 10 3 × shorter 'warm up' time, has fewer metaparameters, and has an ∼ 100× higher accuracy in predicting the coexisting 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.Reservoir computing is a machine learning approach that is well suited to learning dynamical systems using a short sample of time-series data. It learns the underlying dynamical system so that the trained model serves as a surrogate or a 'digital twin' of the system, and it can reproduce behaviors not contained in the training data set. For chaotic systems, it can reproduce the associated strange attractor and other characteristics. Surprisingly, the reservoir computer can learn attractors of a dynamical that is has not seen when it is trained on time-series data from a single attractor that it has seen. Here, we show that a variant machine learning algorithm, known as a next-generation reservoir computer, can reproduce co-existing attractors and the associated basin of attractor using smaller training data sets and with higher accuracy than a traditional reservoir computer.