Využití umělé inteligence pro řešení parciálních diferenciálních rovnic

Abstract

Nowadays, artificial intelligence is a popular method applied to a wide range of problems. If used for computing solutions of problems connected to partial differential equations, we refer to them as Physics-Informed Neural Networks. The key is to correctly include boundary value conditions into its loss function, which serves as a basis for iteratively changing its parameters. Widening its scope to a class of problems, in which there are problem parameters as variables, we get neural operator, with no need of training it again for any specific values of said parameters.