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 $\sim 1.7\times$ 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.

arXiv comment8 pages, 7 figures

References in corpus (11)

• Next Generation Reservoir Computing
• FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators
• High performance photonic reservoir computer based on a coherently driven passive cavity
• On Explaining the Surprising Success of Reservoir Computing Forecaster of Chaos? The Universal Machine Learning Dynamical System with Contrasts to VAR and DMD
• Rapid Time Series Prediction with a Hardware-Based Reservoir Computer
• Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing
• Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithm
• Model-Size Reduction for Reservoir Computing by Concatenating Internal States Through Time
• Symmetry-Aware Reservoir Computing
• Adding Filters to Improve Reservoir Computer Performance
• Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

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• How more data can hurt: Instability and regularization in next-generation reservoir computing
• Model-free Forecasting of Rogue Waves using Reservoir Computing
• Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing