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Sampling of integrand for integration using shallow neural network

Мұқаба

Дәйексөз келтіру

Толық мәтін

Аннотация

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.

Авторлар туралы

Alexander Ayriyan

Joint Institute for Nuclear Research; Alikhanyan National Science Laboratory; Dubna State University

Email: ayriyan@jinr.ru
ORCID iD: 0000-0002-5464-4392

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

6 Joliot-Curie St, Dubna, 141980, Russian Federation; 2 Alikhanyan Brothers St, Yerevan, 0036, Republic of Armenia; 19 Universitetskaya St, Dubna, 141980, Russian Federation

Hovik Grigorian

Joint Institute for Nuclear Research; Alikhanyan National Science Laboratory; Dubna State University; Yerevan State University

Email: hovik.grigorian@gmail.com
ORCID iD: 0000-0002-0003-0512

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

6 Joliot-Curie St, Dubna, 141980, Russian Federation; 2 Alikhanyan Brothers St, Yerevan, 0036, Republic of Armenia; 19 Universitetskaya St, Dubna, 141980, Russian Federation; 1 Alex Manoogian St, Yerevan, 0025, Republic of Armenia

Vladimir Papoyan

Joint Institute for Nuclear Research; Alikhanyan National Science Laboratory; Dubna State University

Хат алмасуға жауапты Автор.
Email: vlpapoyan@jinr.ru
ORCID iD: 0000-0003-0025-5444

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

6 Joliot-Curie St, Dubna, 141980, Russian Federation; 2 Alikhanyan Brothers St, Yerevan, 0036, Republic of Armenia; 19 Universitetskaya St, Dubna, 141980, Russian Federation

Әдебиет тізімі

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  10. Kişi, Ö. & Uncuoǧlu, E. Comparison of three back-propagation training algorithms for two case studies. Indian Journal of Engineering and Materials Sciences 12, 434-442 (Oct. 2005).
  11. Jiawei Han, M. K. & Pei, J. Data mining: concepts and techniques Third Edition. 703 pp. doi: 10.1016/c2009-0-61819-5 (Elsevier Inc., 225 Wyman Street, Waltham, MA 02451, USA, 2012).
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