The defining stage of the process of solving ill-posed inverse problems is the choice of the regularization parameter

Introduction
The development of modern measurement, control, management and diagnostic systems is characterized by increasing requirements for quality indicators, expanding functionality, and increasing complexity of research and design tasks during their creation. As a rule, the basis for the functioning of these systems are methods and means for processing experimental data and computer implementation of mathematical models of dynamic objects (elements, links, blocks, circuits, etc.) that are components of the systems. [1, 2]
Methods for solving inverse dynamics problems are based on the use of optimization algorithms, the implementation of which can be difficult due to the complexity of search procedures, in particular due to the nonlinear dependence of the minimized functional on the model parameters. The increasing complexity of models and difficulties in processing experimental data lead to the need to consider methods for constructing alternative forms of representing dynamic models and further developing methods for solving inverse problems of dynamics. [3]
The most common and effective in practice models for the task of interpreting observational results are Fredholm integral equations of the 1st kind - for the case of spatially distributed input signals, as well as Volterra integral equations of the 1st kind - in the case of dynamic interpretation problems. Problems of solving equations of this class are ill-posed (incorrect), i.e. refer to tasks of increased difficulty that require the fulfillment of specific correctness conditions. These difficulties are aggravated when solving nonlinear interpretation problems described by nonlinear integral equations of the first kind. [4, 5]
The defining stage of the process of solving ill-posed inverse problems is the choice of the regularization parameter. When solving nonlinear integral equations of the first kind, methods for finding the optimal regularization parameter for linear problems may not work. The method of model experiments for finding the regularization parameter is considered, and the possibilities of its application in various variants of methods for solving the interpretation problem are explored. [6]