Аннотация:

An algorithm based on machine learning for solving the problem of boundary control for a complex heat transfer model is considered. The control is a vector function included in the boundary conditions multiplicatively. The system consists of the heat equation and $P_1$ -- approximation of the radiative transfer equation. The solution of the control problem is modeled using the principle "bang-bang".

Based on the numerical-analytical solution of a direct non-stationary nonlinear problem using the FreeFem++ software package, a dataset for machine learning is formed in order to predict the quality functional that characterizes the smooth-ing of the temperature field to the specified field by the input parameters of the model. The solvability of the control prob-lem is proved, necessary optimality conditions are obtained, and a numerical algorithm to find the control function is considered. A neural network optimization problem is formu-lated to determine the multidimensional boundary control. The stochastic method is used to solve the optimization problem. A comparative analysis of the solution of the inverse problem obtained using machine learning with the calculations obtained by solving the optimality system in the case of one boundary control is carried out. The potential of machine learning for the problems of parameters recovery in physical medium is shown.