Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)4009810.22363/2658-4670-2024-32-1-38-47GFROYOArticlesСтатьиResearch ArticleSampling of integrand for integration using shallow neural networkСпособ формирования обучающей выборки для вычисления интеграла с использованием нейронной сетиhttps://orcid.org/0000-0002-5464-4392AyriyanAlexander S.АйриянА. С.

PhD in Physics and Mathematics, Head of sector of the Division of Computational Physics of JINR, Assistant professor of Department of Distributed Information Computing Systems of Dubna State University; Senior Researcher of AANL

ayriyan@jinr.ruhttps://orcid.org/0000-0002-0003-0512GrigorianHovik A.ГригорянО. А.

Candidate of Physical and Mathematical Sciences, Senior Researcher of JINR; Senior Researcher of AANL (YerPhI); Assistant professor of Dubna State University; assistant professor of Yerevan State University

hovik.grigorian@gmail.comhttps://orcid.org/0000-0003-0025-5444PapoyanVladimir V.ПапоянВ. В.

Junior researcher of JINR, Junior researcher of AANL (YerPhI), PhD student of Dubna State University

vlpapoyan@jinr.ruJoint Institute for Nuclear ResearchОбъединённый институт ядерных исследованийAlikhanyan National Science LaboratoryНациональная научная лаборатория им. А. АлиханянаDubna State UniversityГосударственный университет «Дубна»Yerevan State UniversityЕреванский государственный университет30062024321VOL 32, NO1 (2024)ТОМ 32, №1 (2024)384719072024Copyright ©; 2024, Ayriyan A.S., Grigorian H.A., Papoyan V.V.Copyright ©; 2024, Айриян А.С., Григорян О.А., Папоян В.В.2024Ayriyan A.S., Grigorian H.A., Papoyan V.V.Айриян А.С., Григорян О.А., Папоян В.В.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/40098

Inthispaper,westudytheeffectofusingtheMetropolis-Hastingsalgorithmforsamplingtheintegrand on the accuracy of calculating the value of the integral with the use of shallow neural network. In addition, a hybrid method for sampling the integrand is proposed, in which part of the training sample is generated by applying the Metropolis-Hastings algorithm, and the other part includes points of a uniform grid. Numerical experiments show that when integrating in high-dimensional domains, sampling of integrands both by the Metropolis-Hastings algorithm and by a hybrid method is more efficient with respect to the use of a uniform grid.

В настоящей работе исследуется применение алгоритма Метрополиса-Гастингса при формировании обучающей выборки для нейросетевой аппроксимации подынтегральной функции и его влияние на точность вычисления значения интеграла. Предложен гибридный способ формирования обучающего множества, в рамках которого часть выборки генерируется посредством применения алгоритма Метрополиса-Гастингса, а другая часть включает в себя узлы равномерной сетки. Численные эксперименты показывают, что при интегрировании в областях больших размерностей предложенный способ является более эффективным относительно узлов равномерной сетки.

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