On the Equivalence of Real Dynamic Process and Its Neural Network Quadratic Models

Abstract

A dynamic process defined by its own time series is considered. Using the methods of qualitative recurrent analysis, the dimension of the embedding space and the optimal time delay of the specified series are determined. Using these characteristics, a neural network with a quadratic activation function is modeled. The simulation result is presented in the form of a system of neural ODEs. After that, the Lyapunov exponents of the real dynamic system and its neural network model are calculated. Then the closeness of these exponents for a real system and its model makes it possible to judge the adequacy (equivalence) of both dynamic processes. Examples are given.

Keywords

• system of ordinary autonomous differential equations
• quadratic activation function
• neural network
• lyapunov exponents