Controlling dynamical systems into unseen target states using machine learning

Abstract

Controlling nonlinear dynamical systems is a central task in many different areas of science and engineering. Combining previous work on controlling chaotic systems to arbitrary states [1] and extrapolating the system behavior into unseen parameter regions [2] using machine learning, we present here a novel, model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly different and complex dynamics. Leveraging a parameter-aware realization of next-generation reservoir computing (NGRC), our approach accurately predicts system behavior in unobserved parameter regimes, enabling control over transitions to arbitrary target states utilizing a new prediction evaluation and selection scheme [3]. By extending the applicability of machine learning-based control mechanisms to previously inaccessible target dynamics, this methodology opens the door to transformative new applications while maintaining exceptional efficiency. Our results highlight reservoir computing as a powerful alternative to traditional methods for dynamic system control.

[1] A. Haluszczynski & C. Räth, Sci Rep 11, 12991 (2021) [2] D. Köglmayr & C. Räth, Sci Rep 14, 507 (2024) [3] D. Köglmayr, A. Haluszczynski & C. Räth, Advanced Intelligent Systems, e202501319, doi: https://doi.org/10.1002/aisy.202501319 (2026)