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

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.

Tailored Forecasting from Short Time Series via Meta-learning

Machine learning (ML) models can be effective for forecasting the dynamics of unknown systems from time-series data, but they often require large amounts of data and struggle to generalize across systems with varying dynamics. Combined, these issues make forecasting from short time series particularly challenging. To address this problem, we introduce Meta-learning for Tailored Forecasting from Related Time Series (METAFORS), which uses related systems with longer time-series data to supplement limited data from the system of interest. By leveraging a library of models trained on related systems, METAFORS builds tailored models to forecast system evolution with limited data. Using a reservoir computing implementation and testing on simulated chaotic systems, we demonstrate METAFORS' ability to predict both short-term dynamics and long-term statistics, even when test and related systems exhibit significantly different behaviors and the available data are scarce, highlighting its robustness and versatility in data-limited scenarios.