Machine-learning-coined noise induces energy-saving synchrony.

Noise-induced synchronization is a pervasive phenomenon observed in a multitude of natural and engineering systems. Here, we devise a machine learning framework with the aim of devising noise controllers to achieve synchronization in diverse complex physical systems. We find the implicit energy regularization phenomenon of the formulated framework that engenders energy-saving artificial noise and we rigorously elucidate the underlying mechanism driving this phenomenon.

Higher-order Granger reservoir computing: simultaneously achieving scalable complex structures inference and accurate dynamics prediction.

Recently, machine learning methods, including reservoir computing (RC), have been tremendously successful in predicting complex dynamics in many fields. However, a present challenge lies in pushing for the limit of prediction accuracy while maintaining the low complexity of the model. Here, we design a data-driven, model-free framework named higher-order Granger reservoir computing (HoGRC), which owns two major missions: The first is to infer the higher-order structures incorporating the idea of Granger causality with the RC, and, simultaneously, the second is to realize multi-step prediction by feeding the time series and the inferred higher-order information into HoGRC.

Tipping Point Detection Using Reservoir Computing.

Detection in high fidelity of tipping points, the emergence of which is often induced by invisible changes in internal structures or/and external interferences, is paramountly beneficial to understanding and predicting complex dynamical systems (CDSs). Detection approaches, which have been fruitfully developed from several perspectives (e.g.

Leveraging neural differential equations and adaptive delayed feedback to detect unstable periodic orbits based on irregularly sampled time series.

Detecting unstable periodic orbits (UPOs) based solely on time series is an essential data-driven problem, attracting a great deal of attention and arousing numerous efforts, in nonlinear sciences. Previous efforts and their developed algorithms, though falling into a category of model-free methodology, dealt with the time series mostly with a regular sampling rate. Here, we develop a data-driven and model-free framework for detecting UPOs in chaotic systems using the irregularly sampled time series.

Detecting unstable periodic orbits based only on time series: When adaptive delayed feedback control meets reservoir computing.

In this article, we focus on a topic of detecting unstable periodic orbits (UPOs) only based on the time series observed from the nonlinear dynamical system whose explicit model is completely unknown a priori. We articulate a data-driven and model-free method which connects a well-known machine learning technique, the reservoir computing, with a widely-used control strategy of nonlinear dynamical systems, the adaptive delayed feedback control. We demonstrate the advantages and effectiveness of the articulated method through detecting and controlling UPOs in representative examples and also show how those configurations of the reservoir computing in our method influence the accuracy of UPOs detection.

Emergent dynamics of coordinated cells with time delays in a tissue.

In this article, we investigate the emergence of tissue dynamics with time delays of diffusion. Such emergent dynamics, describing the tissue homeostasis, usually correspond to particular tissue functions, which are attracting a tremendous amount of attention from both communities of mathematical modeling and systems biology. Specifically, in addition to the within-cell genome dynamics and the diffusion among the cells, we consider several types of time delays of diffusion present in the coordinated cells.