The paper discusses the connection of Taylor maps and polynomial neural networks (PNN) for numerical solving of the ordinary differential equations (ODEs). Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics of these equations. It is shown that proposed PNN architecture can provide better accuracy with less computational time in comparison with traditional numerical solvers. Moreover, neural network derived from the ODEs can be used for simulation of system dynamics with different initial conditions, but without training procedure. Besides, if the equations are unknown, the weights of the PNN can be fitted in a data-driven way. In the paper, we describe the connection of PNN with differential equations theoretically along with the examples for both dynamics simulation and learning with data.
Original languageEnglish
Title of host publication24th European Conference on Artificial Intelligence, 29 August–8 September 2020, Santiago de Compostela, Spain – Including 10th Conference on Prestigious Applications of Artificial Intelligence (PAIS 2020)
EditorsGiuseppe De Giacomo, Alejandro Catala, at al.
PublisherIOS Press
Number of pages8
ISBN (Electronic)978-1-64368-101-6
ISBN (Print)978-1-64368-100-9
Publication statusPublished - 27 Aug 2020
Event24th European Conference on Artificial Intelligence - Сантьяго де Компостела
Duration: 29 Aug 20208 Sep 2020
Conference number: 24

Publication series

NameFrontiers in Artificial Intelligence and Applications
PublisherIOS Press
ISSN (Print)0922-6389


Conference24th European Conference on Artificial Intelligence
Abbreviated titleECAI
CityСантьяго де Компостела

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