Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation

In this paper, we propose a new mathematical model of language interactions considering bilingualism. We assume diffusive and convective language spreads with language exchange terms. The resulting model consists of a coupled system of partial differential equations for three functions. We develop a...

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Главные авторы:	Tyrylgin, A. A., Тырылгин, А. А.
Формат:	Статья
Язык:	English
Опубликовано:	2023
Темы:	Partial learning Discretization Multicontinuum problems Multiscale problems
Online-ссылка:	https://dspace.ncfu.ru/handle/20.500.12258/23478
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record_format	dspace
spelling	ir-20.500.12258-234782025-02-12T08:34:50Z Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation Tyrylgin, A. A. Тырылгин, А. А. Partial learning Discretization Multicontinuum problems Multiscale problems In this paper, we propose a new mathematical model of language interactions considering bilingualism. We assume diffusive and convective language spreads with language exchange terms. The resulting model consists of a coupled system of partial differential equations for three functions. We develop a finite element approximation of the mathematical model using implicit and partially explicit time schemes. In addition, we present a partial learning approach for this problem using a partially explicit discretization. In this method, we train a Deep Neural Network to predict the values of the difficult-to-compute (implicit) part of the solution at some observed points. We then perform linear temporal interpolation and spatial interpolation using the Proper Orthogonal Decomposition (POD) and the Discrete Empirical Interpolation Method (DEIM). To test the proposed approach and the model, we consider two model problems. Each of them simulates different language situations. For each problem, we compute the relative errors of the proposed approach and define the different parts of the error. The numerical results show that the proposed approach can provide good accuracy while reducing computational costs. 2023-05-12T13:07:53Z 2023-05-12T13:07:53Z 2023 Статья Ammosov, D.A., Stepanov, S.P., Tyrylgin, A.A., Malysheva, N.V., Zamorshchikova, L.S. Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation // Journal of Computational and Applied Mathematics. - 2023. - 425, № 115034. - DOI: 10.1016/j.cam.2022.115034 http://hdl.handle.net/20.500.12258/23478 en Journal of Computational and Applied Mathematics application/pdf application/pdf
institution	СКФУ
collection	Репозиторий
language	English
topic	Partial learning Discretization Multicontinuum problems Multiscale problems
spellingShingle	Partial learning Discretization Multicontinuum problems Multiscale problems Tyrylgin, A. A. Тырылгин, А. А. Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation
description	In this paper, we propose a new mathematical model of language interactions considering bilingualism. We assume diffusive and convective language spreads with language exchange terms. The resulting model consists of a coupled system of partial differential equations for three functions. We develop a finite element approximation of the mathematical model using implicit and partially explicit time schemes. In addition, we present a partial learning approach for this problem using a partially explicit discretization. In this method, we train a Deep Neural Network to predict the values of the difficult-to-compute (implicit) part of the solution at some observed points. We then perform linear temporal interpolation and spatial interpolation using the Proper Orthogonal Decomposition (POD) and the Discrete Empirical Interpolation Method (DEIM). To test the proposed approach and the model, we consider two model problems. Each of them simulates different language situations. For each problem, we compute the relative errors of the proposed approach and define the different parts of the error. The numerical results show that the proposed approach can provide good accuracy while reducing computational costs.
format	Статья
author	Tyrylgin, A. A. Тырылгин, А. А.
author_facet	Tyrylgin, A. A. Тырылгин, А. А.
author_sort	Tyrylgin, A. A.
title	Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation
title_short	Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation
title_full	Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation
title_fullStr	Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation
title_full_unstemmed	Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation
title_sort	partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: language interactions simulation
publishDate	2023
url	https://dspace.ncfu.ru/handle/20.500.12258/23478
work_keys_str_mv	AT tyrylginaa partiallearningusingpartiallyexplicitdiscretizationformulticontinuummultiscaleproblemswithlimitedobservationlanguageinteractionssimulation AT tyrylginaa partiallearningusingpartiallyexplicitdiscretizationformulticontinuummultiscaleproblemswithlimitedobservationlanguageinteractionssimulation
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Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation

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