Abstract:

The numerical solution of the problem of optimal control of the non-stationary flow of a viscous, heat-conducting compressible medium in the one-dimensional case is considered., The initial state velocity and velocity at the right boundary are used as control. To solve the problem, the PINN method, is used. To do this, the problem of minimizing a quadratic functional is solved. The functional includes terms for the residuals of the equations, boundary and initial conditions, and also, for the inverse problem, additional information. Numerical experiments were performed in cases where the velocity, density and temperature separately are minimized to the given functions.  The parameters of the medium correspond to the physical parameters of real gases at high Reynolds numbers, $Re=1.5\cdot10^7-2.4\cdot10^8$, and Peclet numbers, $Pe=3\cdot10^7-1.6\cdot10^8$. The method allows to solve numerically complex nonlinear problems of optimal control without discretization, linearization and solving optimality systems.