Data-driven discrete fractional chaotic systems, new numerical schemes and deep learning

Parameter estimation is important in data-driven fractional chaotic systems. Less work has been reported due to challenges in discretization of fractional calculus operators. In this paper, several numerical schemes are newly derived for delay fractional difference equations of Caputo and Riemann-Liouville types. Then, loss functions are constructed and unknown parameters of the discrete fractional chaotic system are estimated by a neural network method. Parameter estimation results demonstrate high accuracy compared with real values. Robust analysis is provided under different noise levels. It can be concluded that this paper provides an efficient deep learning method based on fractional discrete-time systems.