An algorithm for estimating the deviation between regularized and exact solutions in inverse problems
Abstract
This work is devoted to the construction of an algorithm for checking the existence of a 1:1 linear correlation between the measured and calculated data of unknown functions of a mathematical model. The inverse problem is considered: by the values of the unknown functions of the mathematical model, measured at different times, to determine the values of its parameters. The direct problem is solved with parameter values that are elements of the regularized solution vector. Solutions of the direct problem are functions that depend on time. The calculated data are defined as the values of these functions at the corresponding time points. The Nash-Sutcliffe efficiency and the Pearson correlation coefficient were used to determine the existence of a 1:1 linear correlation between the measured and calculated data. As a numerical example, the inverse problem of restoring the parameters of a mathematical model describing the kinetics of the oil refining process is considered. As a result of the calculations, the existence of a 1:1 linear correlation between the measured and calculated concentrations of substances was determined. This work is considered as an additional step to recheck the regularized approximation to the exact solution of the inverse problem. In the future, the developed algorithm was included in our method for solving inverse problems for more reliable confirmation of the possibility of using a controlled solution instead of an exact one.
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