Застосування згорткових нейронних мереж для розв’язання диференціального рівняння Гельмгольця

Abstract

This work is devoted to developing and training a convolutional neural network to model acoustic wave distribution inside the simplified human skull in 2 dimensions. The neural network is trained in a fixed-point iteration manner, where at each iteration the PDE loss is minimized. The PDE is defined to be an inhomogeneous Helmholtz differential equation where the discretization and derivatives computation is performed by Fourier spectral method. The resulting method allows to compute the solution with float precision faster than classical methods.