Datasets for learning of unknown characteristics of dynamical systems

Area of Science:

• Dynamical systems analysis
• Time series analysis
• Machine learning for signal processing

Background:

• Understanding biological signals requires analyzing their underlying dynamical systems.
• Time series data from physiological processes offer insights into system dynamics.
• Characterizing dynamical systems is crucial for interpreting complex biological signals.

Purpose of the Study:

• To propose novel datasets for machine learning (ML) analysis of dynamical systems.
• To enable the characterization of unknown dynamical systems from observed time series.
• To facilitate the application of deep learning techniques to time series data from various dynamical systems.

Main Methods:

• Generation of 33,000 time series from 15 distinct dynamical systems (chaotic and non-chaotic).
• Classification of non-chaotic systems into periodic, quasi-periodic, and non-periodic categories.
• Technical validation using deep learning models, including recurrent neural networks (RNNs) with long short-term memory (LSTM) and convolutional neural networks (CNNs).

Main Results:

• Demonstrated the utility of the proposed datasets in machine learning classification tasks.
• Successfully applied deep learning models to differentiate characteristics of dynamical systems from time series.
• Validated the effectiveness of LSTMs and CNNs in analyzing complex time series data.

Conclusions:

• The developed datasets are valuable resources for training ML models to understand dynamical systems.
• Machine learning, particularly deep learning, can effectively uncover characteristics of dynamical systems from time series data.
• This work advances the analysis of biological signals and the understanding of physiological processes.