Artificial neural network as a universal model of nonlinear dynamical systems

Standard

Artificial neural network as a universal model of nonlinear dynamical systems. / Kuptsov, Pavel V.; Kuptsova, Anna V.; Stankevich, Nataliya V.

In: Russian Journal of Nonlinear Dynamics, Vol. 17, No. 1, 2021, p. 5-21.

Research output: Contribution to journal › Article › peer-review

Author

Kuptsov, Pavel V. ; Kuptsova, Anna V. ; Stankevich, Nataliya V. / Artificial neural network as a universal model of nonlinear dynamical systems. In: Russian Journal of Nonlinear Dynamics. 2021 ; Vol. 17, No. 1. pp. 5-21.

BibTeX

@article{e64b1149117945f19e08c9cbd341a99d,

title = "Artificial neural network as a universal model of nonlinear dynamical systems",

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 R{\"o}ssler 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.",

keywords = "Dynamical system, Lyapunov exponents, Neural network, Numerical solution, Universal approximation theorem",

author = "Kuptsov, {Pavel V.} and Kuptsova, {Anna V.} and Stankevich, {Nataliya V.}",

note = "Kuptsov P. V., Kuptsova A. V., Stankevich N. V., Artificial Neural Network as a Universal Model of Nonlinear Dynamical Systems, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 1, pp. 5-21",

year = "2021",

doi = "10.20537/ND210102",

language = "English",

volume = "17",

pages = "5--21",

journal = "Russian Journal of Nonlinear Dynamics",

issn = "2658-5324",

publisher = "Institute of Computer Science",

number = "1",

}

RIS

TY - JOUR

T1 - Artificial neural network as a universal model of nonlinear dynamical systems

AU - Kuptsov, Pavel V.

AU - Kuptsova, Anna V.

AU - Stankevich, Nataliya V.

N1 - Kuptsov P. V., Kuptsova A. V., Stankevich N. V., Artificial Neural Network as a Universal Model of Nonlinear Dynamical Systems, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 1, pp. 5-21

PY - 2021

Y1 - 2021

N2 - 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 Rössler 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.

AB - 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 Rössler 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.

KW - Dynamical system

KW - Lyapunov exponents

KW - Neural network

KW - Numerical solution

KW - Universal approximation theorem

UR - http://www.scopus.com/inward/record.url?scp=85105223065&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/049be667-74e4-321c-9acf-46ebd7262e30/

U2 - 10.20537/ND210102

DO - 10.20537/ND210102

M3 - Article

AN - SCOPUS:85105223065

VL - 17

SP - 5

EP - 21

JO - Russian Journal of Nonlinear Dynamics

JF - Russian Journal of Nonlinear Dynamics

SN - 2658-5324

IS - 1

ER -

ID: 86482829