On quasiclassical variational functionals for the wave equation

S. G. Shorokhov

Peoples' Friendship University of Russia named after Patrice Lumumba, Moscow

Abstract: We consider the problem of constructing a quasiclassical variational functional for a one-dimensional homogeneous wave equation in a pentagon-shaped domain. Using the variational method for hyperbolic equations proposed by V. M. Filippov, we obtain a variational functional involving path and iterated integrals in the characteristic variables. This form of the variational functional is adapted for training neural networks that approximate solutions of boundary-value problems in mathematical physics, and increases the efficiency and speed of learning.

Keywords: variational principle, wave equation, neural network, loss functional

UDC: 517.972.7; 004.032.26

MSC: 35A15, 68T07

DOI: 10.36535/2782-4438-2025-245-113-123