Tensor Network Modeling of Electronic Structure of Semiconductor Nanoparticles and Sensory Effect of Layers Based on Them

Vladimir S. Posvyanskii, Valeria L. Bodneva, Andrei V. Chertkov, Kairat S. Kurmangaleev, Maria I. Ikim, Vasily B. Novozhilov (), Ivan V. Oseledets and Leonid I. Trakhtenberg
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Vladimir S. Posvyanskii: N.N. Semenov Federal Research Center for Chemical Physics RAS, 4 Kosygin Street, Moscow 119991, Russia
Valeria L. Bodneva: N.N. Semenov Federal Research Center for Chemical Physics RAS, 4 Kosygin Street, Moscow 119991, Russia
Andrei V. Chertkov: Artificial Intelligence Research Institute, 32 Bld. 1 Kutuzovsky Ave., Moscow 121170, Russia
Kairat S. Kurmangaleev: N.N. Semenov Federal Research Center for Chemical Physics RAS, 4 Kosygin Street, Moscow 119991, Russia
Maria I. Ikim: N.N. Semenov Federal Research Center for Chemical Physics RAS, 4 Kosygin Street, Moscow 119991, Russia
Vasily B. Novozhilov: N.N. Semenov Federal Research Center for Chemical Physics RAS, 4 Kosygin Street, Moscow 119991, Russia
Ivan V. Oseledets: Artificial Intelligence Research Institute, 32 Bld. 1 Kutuzovsky Ave., Moscow 121170, Russia
Leonid I. Trakhtenberg: N.N. Semenov Federal Research Center for Chemical Physics RAS, 4 Kosygin Street, Moscow 119991, Russia

Mathematics, 2025, vol. 13, issue 20, 1-14

Abstract: This paper develops mathematical apparatus for the modeling of the electronic structure of semiconductor nanoparticles and the description of sensor response of the layers constructed on their base. The developed technique involves solutions of both the direct and inverse problems. The direct problem involves of the two coupled sets of differential equations, at fixed values of physical parameters. The first of them is the set of equations of chemical kinetics which describes processes occurring at the surface of a nanoparticle. The second involves an equation describing electron concentration distribution inside a nanoparticle. The inverse problem consists of the determination of physical parameters (essentially, reactions rate constants) which provide a good approximation of experimental data when using them to find the solution of the direct problem. The mathematical novelty of this paper is the application of—for the first time, to find the solution of the inverse problem—the new gradient-free optimization methods based on low-rank tensor train decomposition and modern machine learning paradigm. Sensor effect was measured in a dedicated set of experiments. Comparisons of computed and experimental data on sensor effect were carried out and demonstrated sufficiently good agreement.

Keywords: conductivity; sensors; tensor; tensor train; boundary value problem; machine learning; gradient-free optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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