Optimization of the Set of Regularized Solutions in the Coefficient Inverse Problem

This work is devoted to the optimization of the set of possible solutions to the inverse problem, which is solved by the Tikhonov’s regularization method. First, a mathematical model described by a system of ordinary differential equations is investigated. Then, within the framework of the studied model, the inverse problem was posed: to determine the coefficients of this model from the experimental data of the solutions. The Tikhonov’s regularization method was used to solve the inverse problem. As a result, a set of regularized solutions (admissible solutions) is obtained. And finally, to narrow the set of admissible solutions of the inverse problem, we used criteria related to the distribution density of the elements of the set. Specifically, we consider a case that corresponds to a criterion for the set of accepted solutions. As a result, for each case, a subset of the set of feasible solutions is obtained, in which there are solutions of the inverse problem that satisfy the given criterion. In the future, our work proposes a way to restore the parameters of mathematical models in scientific fields in general and in the field of economics, electrical engineering and energy in particular