Applications of Neural-Network Algorithms to Nonlinear Time Series Analysis of Dynamical Optical Systems

Abstract

The techniques of prediction and modeling using a neural network algorithm, preceded by application of noise reduction methods, are shown to be applicable to time series associated with nonlinear dynamical optical systems. The time series generated from a generic dynamical model is used to train a backpropagation, feed forward neural network which is subsequently used to demonstrate strong predictive characteristics. It is demonstrated that such a simple neural network, consisting of fifty neurons, trained using a time series generated from the logistic map in the chaotic regime, produces a self-generated time series which has a maximum positive Lyapunov exponent, χ, which is within six percent of the value obtained from the map, using the same method for determination of χ from the time series. It is also shown that system and measurement noise can be reduced, in the white noise driven logistics map, to within ten percent using an extended Kalman filter algorithm.