Mathematical Modeling on a Physics-Informed Radial Basis Function Network

Dmitry Stenkin and Vladimir Gorbachenko ()
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Dmitry Stenkin: Department of Computer Technologies, Penza State University, Penza 440026, Russia
Vladimir Gorbachenko: Department of Computer Technologies, Penza State University, Penza 440026, Russia

Mathematics, 2024, vol. 12, issue 2, 1-11

Abstract: The article is devoted to approximate methods for solving differential equations. An approach based on neural networks with radial basis functions is presented. Neural network training algorithms adapted to radial basis function networks are proposed, in particular adaptations of the Nesterov and Levenberg-Marquardt algorithms. The effectiveness of the proposed algorithms is demonstrated for solving model problems of function approximation, differential equations, direct and inverse boundary value problems, and modeling processes in piecewise homogeneous media.

Keywords: physics-informed neural networks; partial differential equations; boundary value problem; inverse problems; radial basis function networks; neural network learning; Nesterov method; Levenberg-Marquardt method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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