Training a Neural Network for a Hyperbolic Equation by Using a Quasiclassical Functional
- Authors: Shorokhov S.G.1
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Affiliations:
- Peoples’ Friendship University of Russia named after Patrice Lumumba
- Issue: Vol 237 (2024)
- Pages: 76-86
- Section: Статьи
- URL: https://journal-vniispk.ru/2782-4438/article/view/274740
- DOI: https://doi.org/10.36535/2782-4438-2024-237-76-86
- ID: 274740
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Abstract
We study the problem of constructing a loss functional based on the quasiclassical variational principle for training a neural network, which approximates solutions of a hyperbolic equation. Using the method of symmetrizing operator proposed by V. M. Shalov, for the secondorder
hyperbolic equation, we construct a variational functional of the boundary-value problem, which involves integrals over the domain of the boundary-value problem and a segment of the boundary, depending on first-order derivatives of the unknown function. We demonstrate that the neural network approximating the solution of the boundary-value problem considered can be trained by using the constructed variational functional.
About the authors
Sergey G. Shorokhov
Peoples’ Friendship University of Russia named after Patrice Lumumba
Author for correspondence.
Email: shorokhov-sg@rudn.ru
Russian Federation, Moscow
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