Feoktistov E.F. Regularization of an Ill-Posed Problem Arising When Calculating the Parameters of a Mathematical Model for Optimizing the Composition of a Polymer Composite
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https://doi.org/10.15688/mpcm.jvolsu.2025.3.6
Egor F. Feoktistov
Postgraduate Student, Volgograd State University
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https://orcid.org/0000-0002-1053-0000
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Abstract. The article considers the problem of optimization of the polymer composition, which arises due to the insufficient experimental data on the interactions of ingredients and their effect on the properties of the material. Under conditions of limited data, a method is proposed for estimating unknown parameters of the model used to optimize the composition, such as the vector and matrix of interactions of additives and their effect on the target properties of the polymer composition. To solve the problem, regularization of the ill-posed problem is used, which occurs when trying to find the model parameters based on a limited number of recipes. The main approach is to minimize the norm of the difference between the right and left parts of the system of equations, which allows obtaining approximate values of the sought parameters. The work includes a computational experiment in which recipes from two patents are studied, which illustrates the practical applicability of the proposed method for real polymer compositions. Regularization allows you to correctly estimate the parameters even with incompatible initial data, which makes the method an effective tool for preliminary modeling and reducing the volume of natural experiments in chemical engineering.
Key words: quadratic programming problem, polymer composites, machine learning, small data, ill-posed problems, regularization.
Regularization of an Ill-Posed Problem Arising When Calculating the Parameters of a Mathematical Model for Optimizing the Composition of a Polymer Composite by Feoktistov E.F. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 28 No. 3 2025, pp. 67-75
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