Physics-Informed Neural Networks pro stacionární a tranzientní úlohy

Abstract

Neural networks (NNs) are a useful tool for solving many problems such as classification tasks, data processing, pattern recognition and many more. In recent years, there has been a growing interest in the use of NNs in solving problems involving partial differential equations, which can be very computationally demanding to solve by numerical methods. A promising method for solving such problems are PINNs - Physics-Informed Neural Networks. These NNs incorporate physical laws (conservation laws, boundary conditions, ...) into a loss function that is optimized in the process of training the neural network. In this paper, the basic construction of NNs and the implementation of PINNs for solving different boundary value problems with different types of differential equations are described. Cases in which the conventional PINN implementation does not generate correct results are also presented, and ways in which its performance can be improved are described.