Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing

TL;DR

This paper demonstrates that reservoir computing can generalize to unseen regions of state space in dynamical systems without explicit priors, using a multi-trajectory training scheme that enables out-of-domain predictions.

Contribution

It introduces a multi-trajectory training scheme for reservoir computing that allows generalization to unobserved system behaviors in different basins of attraction.

Findings

Reservoir computing can generalize beyond training data in dynamical systems.

Multi-trajectory training improves out-of-domain prediction capabilities.

Effective modeling of multistable systems with unseen basins.

Abstract

Machine learning techniques offer an effective approach to modeling dynamical systems solely from observed data. However, without explicit structural priors -- built-in assumptions about the underlying dynamics -- these techniques typically struggle to generalize to aspects of the dynamics that are poorly represented in the training data. Here, we demonstrate that reservoir computing -- a simple, efficient, and versatile machine learning framework often used for data-driven modeling of dynamical systems -- can generalize to unexplored regions of state space without explicit structural priors. First, we describe a multiple-trajectory training scheme for reservoir computers that supports training across a collection of disjoint time series, enabling effective use of available training data. Then, applying this training scheme to multistable dynamical systems, we show that RCs trained on trajectories from a single basin of attraction can achieve out-of-domain generalization by capturing system behavior in entirely unobserved basins.