Anna Kuptsova
Publications:
Kuptsov P. V., Kuptsova A. V., Stankevich N. V.
Artificial Neural Network as a Universal Model of Nonlinear Dynamical Systems
2021, Vol. 17, no. 1, pp. 521
Abstract
We suggest a universal map capable of recovering the behavior of a wide range of dynamical
systems given by ODEs. The map is built as an artificial neural network whose weights encode
a modeled system. We assume that ODEs are known and prepare training datasets using the
equations directly without computing numerical time series. Parameter variations are taken into
account in the course of training so that the network model captures bifurcation scenarios of the
modeled system. The theoretical benefit from this approach is that the universal model admits
applying common mathematical methods without needing to develop a unique theory for each
particular dynamical equations. From the practical point of view the developed method can be
considered as an alternative numerical method for solving dynamical ODEs suitable for running
on contemporary neural network specific hardware. We consider the Lorenz system, the Rцssler
system and also the Hindmarch – Rose model. For these three examples the network model
is created and its dynamics is compared with ordinary numerical solutions. A high similarity
is observed for visual images of attractors, power spectra, bifurcation diagrams and Lyapunov
exponents.
