Improving the accuracy of solving inverse problems with inherent errors

The article deals with the issues related to the stability of inverse problems solution with respect to the exact setting of boundary conditions. In practical applications, as a rule, the theoretical form of the boundary conditions functional dependence is undefined or unknown, and there are random measurement errors. Studies have shown that this leads to a significant decrease in the accuracy of the inverse problem solution. In order to improve the accuracy of solving inverse problems, it was proposed to refine the functional form of the boundary conditions using the recognition of the form of the mathematical model of dependence with the subsequent approximation of the behavior of a physical quantity at the boundary by this function. Restoration of the dependence form is performed by the recognition method based on the reverse display. We have given the model examples of implementation in the presence of additive random measurement errors and an unknown form of boundary conditions dependence.