Reconstructing seen and unseen attractors from data via autonomous-mode reservoir computing

Abstract

Reservoir computing is a powerful tool for creating digital twins of a target systems. They can both predict future values of a chaotic timeseries to a high accuracy and also reconstruct the general properties of a chaotic attractor. In this. We show that their ability to learn the dynamics of a complex system can be extended to systems with multiple co-existing attractors, here a four-dimensional extension of the well-known Lorenz chaotic system. Even parts of the phase space that were not in the training set can be explored with the help of a properly-trained reservoir computer. This includes entirely separate attractors, which we call "unseen". Training on a single noisy trajectory is sufficient. Because Reservoir Computers are substrate-agnostic, this allows the creation of conjugate autonomous reservoir computers for any target dynamical systems.