Приближенное решения 2D уравнения Навье-Стокса методом Фурье-нейрооператора

Abstract

The Navier-Stokes equation, along with other equations of hydrogas dynamics, is nontrivial and generally has no analytical solution. Some simplifications make it possible to obtain an analytical solution to this equation, but in practice they often resort to its numerical solution. There are a number of classical methods for this.: finite difference method; finite volume method; finite element method. Classical approaches to solving the Navier-Stokes equation lead to lengthy calculations with the slightest change in equation parameters, initial or boundary conditions. Modern approaches based on neural network models, such as convolutional neural networks, make it possible to optimize the solution of such equations, but they strongly depend on data discretization. The neural Fourier operator avoids this dependence by training the model on data not in the time domain, but in the spectral domain. This approach makes it possible to significantly reduce the time needed to solve the equations of hydrogas dynamics, while maintaining the flexibility of the model