Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing
This work addresses the challenge of reconstructing phase space features for systems with co-existing attractors, which is incremental but extends reservoir computing to new applications in chaotic dynamics.
The paper tackled the problem of inferring unseen attractors in complex dynamical systems from limited data, demonstrating that a reservoir computer can predict the existence of attractors not observed during training using only a single noisy trajectory.
Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy, as well as reconstruct the general properties of a chaotic attractor without requiring a model. In this work, we show that the ability to learn the dynamics of a complex system can be extended to systems with co-existing attractors, here a 4-dimensional extension of the well-known Lorenz chaotic system. We demonstrate that a reservoir computer can infer entirely unexplored parts of the phase space: a properly trained reservoir computer can predict the existence of attractors that were never approached during training and therefore are labelled as unseen. We provide examples where attractor inference is achieved after training solely on a single noisy trajectory.