Dimensionality reduction in inverse diffusion problem by means of numerical optimization methods

Title	Dimensionality reduction in inverse diffusion problem by means of numerical optimization methods
Authors	A. O. Syromyasov¹, D. V. Galkin¹, A. S. Shurshina², M. V. Shamolin³ ¹National Research Ogarev Mordovia State University ²Bashkir State University ³Lomonosov Moscow State University
Annotation	Article discusses the problem of determination of variable diffusion coefficient when the average concentration of admixture in organic film is measured and known in some moments of time. The problem is hard to solve for two reasons. First, the diffusion coefficient depends on large amount of parameters. Second, the dependence of average concentration on these parameters is complicated. The hypothesis is proposed that allows to find some of the parameters independently from others. Results of corresponding numerical experiment are stated.
Keywords	inverse diffusion problem, least squares method, numerical optimization.
Citation	Syromyasov A. O., Galkin D. V., Shurshina A. S., Shamolin M. V. ''Dimensionality reduction in inverse diffusion problem by means of numerical optimization methods'' [Electronic resource]. Proceedings of the XIV International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 9-12, 2019). Saransk: SVMO Publ, 2019. - pp. 156-159. Available at: https://conf.svmo.ru/files/2019/papers/paper41.pdf. - Date of access: 23.11.2024.