Reservoir computing is a machine learning method that is closely linked to dynamical
systems theory. This connection is highlighted in a brief introduction to the general concept …

Reservoir computing is a machine learning framework that has been shown to be able to
replicate the chaotic attractor, including the fractal dimension and the entire Lyapunov …

This paper focuses on learning the dynamics of time delay systems from trajectory data and
proposes the use of the maximal Lyapunov exponent (MLE) as an indicator to describe the …

In this article, the connection between time delay systems and time delay neural networks
(TDNNs) is presented from a continuous-time perspective. TDNNs are utilized to learn the …

Recurrent neural networks excel at predicting and generating complex high-dimensional
temporal patterns. Due to their inherent nonlinear dynamics and memory, they can learn …

In this paper, we focus on learning the time delay and nonlinearity of autonomous dynamical
systems using trainable time delay neural networks. We demonstrate that, with delays …

Prediction of intermittent chaos is an important issue when detecting the precursors of
extreme events such as catastrophic phenomena. We numerically investigate the time …