519.651 Application of Bethe energy approximation to determine the numerical characteristics of codes on a graph structures
Tlibekov A. T. (Bauman Moscow State Technical University)
INVERSE PROBLEM, FRACTIONAL POWER SERIES, GLOBAL OPTIMIZATION, IDENTIFICATION, LIPSCHITZ CONDITION, SEARCH SPACE, UNCERTAINTY INTERVAL, GOAL FUNCTION
doi: 10.18698/2309-3684-2025-1-116133
An algorithm for identifying the parameters of a mathematical model using experimental data in the form of a matrix of independent variables and a vector of the studied experimental responses is considered. The mathematical model is nonlinear, and the algorithm for solving it is unstable. The conditions under consideration are typical for inverse problems of mathematical physics. The need to solve similar problems is caused by the results of field experiments or information stored in the databases of the characteristics of the production processes of a machine-building plant, which is used for optimal design of a new or modernization of existing production. The mathematical model approximating the independent variables and the studied responses is represented by a modified fractional power series of several variables. An algorithm for searching for coefficients and degrees of a fractional power series has been developed. An iterative method containing blocks of random search, global optimization based on the Lipschitz condition and solving a system of linear algebraic equations is used. The algorithm has been tested. The effectiveness was assessed by the maximum relative error in calculating the studied responses and by the time of calculations.
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