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

2025-06-05

AI Summary

Data-driven modeling of dynamical systems often suffers from poor generalization—particularly in the absence of structural priors, where extrapolation to unexplored regions of state space (e.g., unseen basins of attraction) remains challenging. Method: We propose a multi-trajectory joint training paradigm for reservoir computing (RC), enabling, for the first time, strong generalization across distinct basins of attraction without relying on explicit dynamical assumptions or prior knowledge; training requires trajectories solely from a single basin. Contribution/Results: Evaluated on multistable systems, our approach achieves high-accuracy prediction of dynamics in entirely unseen basins. It fundamentally extends RC’s generalization capability beyond its traditional limits—achieving prior-free, cross-basin, and data-efficient extrapolation. This establishes a new paradigm for interpretable modeling and long-term forecasting of complex nonlinear systems.

Technology Category

• Machine Learning: Multimodal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Generalizing to unseen state space without structural priors
• Training reservoir computers on disjoint time series data
• Achieving out-of-domain generalization in multistable systems

Innovation

• Reservoir computing generalizes without structural priors
• Multiple-trajectory training enhances data utilization
• Captures unobserved basins in multistable systems