Declan A. Norton

Declan A. Norton, Yuanzhao Zhang, Michelle Girvan

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.

Declan A. Norton, Edward Ott, Andrew Pomerance et al.

Machine learning models can effectively forecast dynamical systems from time-series data, but they typically require large amounts of past data, making forecasting particularly challenging for systems with limited history. To overcome this, we introduce Meta-learning for Tailored Forecasting using Related Time Series (METAFORS), which generalizes knowledge across systems to enable forecasting in data-limited scenarios. By learning from a library of models trained on longer time series from potentially related systems, METAFORS builds and initializes a model tailored to short time-series data from the system of interest. Using a reservoir computing implementation and testing on simulated chaotic systems, we demonstrate that METAFORS can reliably predict both short-term dynamics and long-term statistics without requiring contextual labels. We see this even when test and related systems exhibit substantially different behaviors, highlighting METAFORS' strengths in data-limited scenarios.