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Mathematical Modeling on a Physics-Informed Radial Basis Function Network

Author

Listed:
  • Dmitry Stenkin

    (Department of Computer Technologies, Penza State University, Penza 440026, Russia)

  • Vladimir Gorbachenko

    (Department of Computer Technologies, Penza State University, Penza 440026, Russia)

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.

Suggested Citation

  • Dmitry Stenkin & Vladimir Gorbachenko, 2024. "Mathematical Modeling on a Physics-Informed Radial Basis Function Network," Mathematics, MDPI, vol. 12(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:241-:d:1317500
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    References listed on IDEAS

    as
    1. Chih-Yu Liu & Cheng-Yu Ku, 2023. "A Novel ANN-Based Radial Basis Function Collocation Method for Solving Elliptic Boundary Value Problems," Mathematics, MDPI, vol. 11(18), pages 1-19, September.
    2. Zhixiang Liu & Yuanji Chen & Ge Song & Wei Song & Jingxiang Xu, 2023. "Combination of Physics-Informed Neural Networks and Single-Relaxation-Time Lattice Boltzmann Method for Solving Inverse Problems in Fluid Mechanics," Mathematics, MDPI, vol. 11(19), pages 1-29, October.
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