DEEP WAVE EQUATION MODELING WITH QUASICLASSICAL VARIATIONAL PRINCIPLE

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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.