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<p><i>We study the problem of constructing a loss functional for neural network training based on the quasiclassical variational formulation of the boundary value problem for the one-dimensional wave equation, proposed by V. M. Filippov. We derive the variational functional that contains no partial derivatives of the solution or repeated integrals. We show that the obtained quasiclassical loss functional has certain advantages over the residual loss functional when training a neural network. Bibliography: 20 titles. Illustrations: 3 figures.</i></p>

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DEEP WAVE EQUATION MODELING WITH QUASICLASSICAL VARIATIONAL PRINCIPLE

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • S. G. Shorokhov

摘要

We study the problem of constructing a loss functional for neural network training based on the quasiclassical variational formulation of the boundary value problem for the one-dimensional wave equation, proposed by V. M. Filippov. We derive the variational functional that contains no partial derivatives of the solution or repeated integrals. We show that the obtained quasiclassical loss functional has certain advantages over the residual loss functional when training a neural network. Bibliography: 20 titles. Illustrations: 3 figures.