Systems of Singular Differential Equations as the Basis for Neural Network Modeling of Chaotic Processes

Abstract

Currently, systems of neural ordinary differential equations (ODEs) have become widespread for modeling various dynamic processes. However, in forecasting tasks, priority remains with the classical neural network approach to building a model. This is due to the fact that by choosing the neural network architecture, a more accurate approximation of the trajectories of a dynamic system can be achieved. It is known that the accuracy of the mentioned approximation significantly depends on the settings of the neural network parameters and their initial values. In this regard, the main idea of the article is that the initial values of the neural network parameters are taken to be equal to the parameters of the neural ODE system obtained by modeling the same process, which will then be simulated using a neural network. Subsequently, the singular ODE system was used to adjust the parameters of the LSTM (Long Short Term Memory) neural network. The results obtained were used to model the process of epilepsy.

Keywords

• time series
• system of differential equations
• compact region of attraction
• neural network