Numerical solution of the system of Navier-Stokes equations in the case of a compressible medium using neural networks
Abstract
The use of the Physics Informed Neural Networks (PINN) method for the numerical solution of a nonstationary nonlinear system of partial differential equations describing the process of motion of a one-dimensional heat-conducting gas is considered. The approach is based on the fact that a neural network approximates the solution of a system of differential equations, while taking into account the physics of the simulated process. The neural network is trained by minimizing a quadratic functional built on the difference between the predicted values and residuals of differential equations, boundary and initial conditions. Different types of approximation of the original equations are discussed in the case when the operator is continuous or discrete in time. An analysis of the presented methods is carried out. Their advantages and disadvantages are indicated.
