Використання фізично-інформованих нейронних мереж в задачах математичної фізики

Abstract

This work will consider a physically informed neural network for solving partial differential equations. The model will be trained in the form of minimizing the linear convolution of the residual function in terms of the equation and the conditions of the problem. Such an approach to building physical models allows you to obtain solutions to such problems with high resolution with a large grid size on which training will take place. It also allows you to solve problems with a supersaturated condition, which conventional numerical methods cannot. The solution results are a relevant study of a new approach to the application of machine learning in physics