Aug 2026· Chaos· Vol 36 8· 0 citations· 14 references
Medicine
TL;DR
A multi-regime RC framework in which multiple readouts are trained under different dynamical conditions and combined through a short observation window to form a trajectory-dependent linear readout enables both regime identification and adaptation to unseen or intermediate dynamics.
Abstract
Accurate prediction of nonlinear dynamical systems becomes particularly challenging when the evolution of the dynamics depends on hidden, time-varying factors that are not directly observable. Although reservoir computing (RC) provides an efficient framework for modeling complex dynamics, standard approaches based on a single trained readout often experience reduced accuracy in such non-autonomous settings. We propose a multi-regime RC framework in which multiple readouts are trained under different dynamical conditions and combined through a short observation window to form a trajectory-dependent linear readout. This enables both regime identification and adaptation to unseen or intermediate dynamics. The method is evaluated on a Duffing oscillator with a time-varying forcing input and a Rössler system driven by chaotic forcing from a Chen system. The results show improved prediction accuracy compared to both regime-specific and single global models trained on data aggregated from multiple regimes.
This letter develops a data-driven control framework for nonlinear ensemble systems using reservoir computing (RC). We consider ensemble control problems, in which the objective is to regulate a large, potentially uncountable, population of systems with unknown dynamics. To address this challenge, we introduce a moment kernelization approach that yields a dual representation and enables a valid finite-dimensional approximation of ensemble dynamics. Building on this reduction, we cast ensemble control synthesis as the approximation of a causal operator that maps moment trajectories to control inputs. We show that continuous-time reservoir systems induce well-defined causal input-output operators with the fading-memory property, providing a principled foundation for learning these feedback operators from moment trajectory data. Based on this theory, we design an RC-based controller trained on input-output moment trajectories and deployed in a closed-loop configuration for tracking and stabilization of nonlinear ensemble systems.
Yuan-Hung Kuan, Lin Tang, Jr-Shin Li· IEEE Control Systems Letters· 0 citations
Multi-step training of sparse, interpretable models of dynamical systems directly from time-series data yields models with accurate short-term dynamics and strong agreement in long-time statistical properties, including mean, variance, and Lyapunov exponents.
This study investigates the capability of deep neural networks to infer the time-evolution of the Rössler system a canonical chaotic oscillator by leveraging initial conditions and forcing parameters as input variables and underscores the need for hybrid approaches to address long-term instability.
A. Fateh, Harrag Abdelmalek, F. Mohamed et al.· International Journal of App...· 0 citations
This work introduces a probabilistic, non-intrusive reduced-order model (ROM) for chaotic dynamical systems, arguing that projecting high-dimensional nonlinear dynamics onto a low-dimensional manifold introduces irreducible uncertainty, compounded by the chaotic attractors and multi-admissible futures inherent to turbulent flows.
Ismaël Zighed, Nicolas Thome, Patrick Gallinari et al.· 0 citations
Reservoir computing has emerged as an efficient machine learning framework for predicting time series generated by dynamical systems. In contrast to other machine and deep learning approaches, a reservoir computing trains only the output layer via linear regression, leaving the reservoir (recurrent layer) untrained. This simplification makes reservoir computers easier to train and more amenable to experimentation. However, because current reservoirs consist of networks of randomly connected nodes and require the optimization of numerous hyperparameters, a framework that precisely explains how reservoir computing operates and how it can be optimized remains missing. Here, we propose a frequency-based reservoir inspired by the brain's oscillatory dynamics and its hierarchy of timescales. The frequency-based reservoir can be interpreted as an ensemble of independent oscillatory units, each processing a portion of the input's frequency content. This allows us to understand the reservoir's internal behavior by modeling it as a single unit driven by an external input. Borrowing from the theory of a nonlinear oscillator forced by complex periodic inputs, we found that units of the frequency-based reservoir selectively amplify and store specific input frequencies, which are then used for prediction. The frequency-based reservoir performs as well as or better than equivalent random reservoirs. Furthermore, the frequency-based approach can be optimized to improve short-term prediction, a property that random reservoirs lack. Finally, we show that the frequency-based reservoir can also predict complex spatiotemporal dynamics. Our results show that reservoir computing can be designed using brain properties and theoretical insights borrowed from the physics of forced nonlinear oscillators.
The complexity of nonlinear dynamical systems can be analyzed using indicators such as Lyapunov exponents or bifurcation diagrams, whose estimation remains challenging and data-intensive in experimental contexts with constraints. At the same time, reservoir computing (RC) has emerged as a powerful tool for chaotic time series prediction, and the associated metric, the normalized mean square error (NMSE), is solely used to evaluate predictive performance. In this work, we demonstrate that the NMSE from an RC-based prediction model can be used as an indicator for system dynamical characterization. We propose a unified, numerical, and experimental approach based on a single-node time-delay reservoir computing architecture implemented around a Mackey-Glass oscillator and a low-cost hardware platform using an Arduino Due board. The approach is evaluated on discrete and continuous dynamical systems. The variations of NMSE as a function of control parameters are systematically compared with those of Lyapunov exponents and bifurcation diagrams. The results show that different transition regimes (periodic, chaotic, and hyperchaotic) can be reproducible in the variation of the NMSE, both numerically and experimentally. Viewed in this dynamical order, our results also reveal a sigmoidal relationship between the NMSE and the largest Lyapunov exponent. Therefore, the NMSE, beyond its classical role as a prediction metric, can be used as a data-driven indicator reflecting the complexity of a target system’s dynamics. This study thus provides an alternative approach for probing dynamical regimes from finite time series, paving the way for embedded neuromorphic tools dedicated to the experimental analysis of complex nonlinear systems.
Evrard Gabin Noutsa Tedjeuzen, Dagobert Wenkack Liedji, K. Lüdge et al.· AIP Advances· 0 citations
