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, removed many algorithm metaparameters and identified 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 103× shorter “warmup” time, has fewer metaparameters, and has an ∼100× 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 01, 2022
- Source ID
- 10.1063/5.0116784
Entities
People
- André Röhm
- Daniel J Gauthier
- Ingo Fischer
Organizations
- Agencia Estatal de Investigación
- Air Force Office of Scientific Research
- Ohio State University
- University of Tokyo