Harnessing machine learning for identifying parameters in fractional chaotic systems

Abstract

This paper investigates data-driven learning techniques for fractional chaotic systems (FCS), specifically those utilizing the Caputo derivative. Three machine learning (ML) methods are employed for parameter estimation: feedforward neural networks (FNN), long short-term memory (LSTM), and gated recurrent units (GRU). Optimization problems are formulated, and the well-known algorithms, Backpropagation Through Time (BPTT) and Adam, are employed to train the weights and parameters of the ML models. Systematic numerical testing reveals that LSTM demonstrates superior recognition performance for undisturbed data, while GRU achieves higher accuracy in the presence of disturbances. This study presents a highly accurate approach for solving parameter inverse problems, with the potential for extending these methods to other fractional systems.