Datasets for learning of unknown characteristics of dynamical systems

Abstract

The ability to uncover characteristics based on empirical measurement is an important step in understanding the underlying system that gives rise to an observed time series. This is especially important for biological signals whose characteristic contributes to the underlying dynamics of the physiological processes. Therefore, by studying such signals, the physiological systems that generate them can be better understood. The datasets presented consist of 33,000 time series of 15 dynamical systems (five chaotic and ten non-chaotic) of the first, second, or third order. Here, the order of a dynamical system means its dimension. The non-chaotic systems were divided into the following classes: periodic, quasi-periodic, and non-periodic. The aim is to propose datasets for machine learning methods, in particular deep learning techniques, to analyze unknown dynamical system characteristics based on obtained time series. In technical validation, three classifications experiments were conducted using two types of neural networks with long short-term memory modules and convolutional layers.