Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing

TL;DR

This paper demonstrates that reservoir computers can infer unseen attractors in chaotic systems from a single noisy trajectory, extending their predictive capabilities to unexplored phase space regions.

Contribution

It introduces a method for reservoir computers to reconstruct and predict unseen attractors in complex systems from minimal data, including noisy trajectories.

Findings

Reservoir computers can predict unseen attractors in a 4D Lorenz system.

Unseen attractors can be inferred after training on a single noisy trajectory.

The method works without requiring prior knowledge of the system's full phase space.

Abstract

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.