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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">concconc</journal-id><journal-title-group><journal-title xml:lang="ru">Железобетонные конструкции</journal-title><trans-title-group xml:lang="en"><trans-title>Reinforced concrete structures</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2949-1622</issn><issn pub-type="epub">2949-1614</issn><publisher><publisher-name>Национальный исследовательский Московский государственный строительный университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22227/2949-1622.2025.1.35-48</article-id><article-id custom-type="elpub" pub-id-type="custom">concconc-69</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ В СТРОИТЕЛЬСТВЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>COMPUTER MODELLING IN CONSTRUCTION</subject></subj-group></article-categories><title-group><article-title>Физически-информированные нейронные сети для задач строительной механики и конструкций: моделирование прогиба однопролетной балки</article-title><trans-title-group xml:lang="en"><trans-title>Physics-Informed Neural Networks for Structural Mechanics and Construction: Modeling the Deflection of a Single-Span Beam Physics-Informed Neural Networks</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0006-6242-8776</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Захаров</surname><given-names>Ф. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Zakharov</surname><given-names>F. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Фёдор Николаевич Захаров, кандидат технических наук, руководитель отдела исследований и разработок</p><p>310030, г. Ханчжоу, район Сиху, ул. Вэньи Вест Роуд, д. 767, Международный центр Сиси, корпус D, 7-й этаж, провинция Чжэцзян</p></bio><bio xml:lang="en"><p>Fedor N. Zakharov, Candidate of Technical Sciences, Head of the Research and Development Department</p><p>767 Wenyi West Road, Xixi International Center, Building D, 7th Floor, Hangzhou, Xihu District, 310030, Zhejiang Province</p></bio><email xlink:type="simple">zaharof2010@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Цзе</surname><given-names>Цянь</given-names></name><name name-style="western" xml:lang="en"><surname>Jie</surname><given-names>Qian</given-names></name></name-alternatives><bio xml:lang="ru"><p>Цянь Цзе, магистр инженерии, генеральный менеджер</p><p>310030, г. Ханчжоу, район Сиху, ул. Вэньи Вест Роуд, д. 767, Международный центр Сиси, корпус D, 7-й этаж, провинция Чжэцзян</p></bio><bio xml:lang="en"><p>Qian Jie, Master of Engineering, General Manager</p><p>767 Wenyi West Road, Xixi International Center, Building D, 7th Floor, Hangzhou, Xihu District, 310030, Zhejiang Province</p></bio><email xlink:type="simple">23539954@qq.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>И</surname><given-names>Сюй</given-names></name><name name-style="western" xml:lang="en"><surname>Yi</surname><given-names>Xu</given-names></name></name-alternatives><bio xml:lang="ru"><p>Сюй И, магистр инженерии, старший инженер</p><p>310027, г. Ханчжоу, район Сиху, ул. Юхантан, д. 866, провинция Чжэцзян</p></bio><bio xml:lang="en"><p>Xu Yi, Master of Engineering, Senior Engineer</p><p>866 Yuhangtang Road, Hangzhou, Xihu District, 310027, Zhejiang Province</p></bio><email xlink:type="simple">23539954@qq.com</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Научно-исследовательский институт Блютаун Леджу Констракшн Менеджмент Ко. Лтд.</institution><country>Китай</country></aff><aff xml:lang="en"><institution>Bluetown Leju Construction Management Co. Ltd. Research Institute</institution><country>China</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Институт архитектурного проектирования и исследований провинции Чжэцзян</institution><country>Китай</country></aff><aff xml:lang="en"><institution>Zhejiang Province Architectural Design and Research Institute</institution><country>China</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>31</day><month>03</month><year>2025</year></pub-date><volume>9</volume><issue>1</issue><fpage>35</fpage><lpage>48</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Захаров Ф.Н., Цзе Ц., И С., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Захаров Ф.Н., Цзе Ц., И С.</copyright-holder><copyright-holder xml:lang="en">Zakharov F.N., Jie Q., Yi X.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.g-b-k.ru/jour/article/view/69">https://www.g-b-k.ru/jour/article/view/69</self-uri><abstract><p>В статье приведены результаты разработки и анализа моделей физически-информированных нейронных сетей (PINN) для расчета прогиба однопролетной балки под действием равномерно распределённой нагрузки. Для обучения модели был синтезирован набор данных на основе аналитических законов строительной механики, включающий параметры: относительная длина участка измерений 𝑙, количество измерительных точек 𝑁, уровень шума R. Обучающий набор данных содержал 1296 строк, описывающих случайные точки в пределах пролета балки. В рамках исследования обучено 480 моделей PINN для оценки влияния веса физической функции потерь, количества измерений и уровня шума на точность предсказаний. Результаты показали, что модели PINN достигают высокой точности R2 ≥ 0,88 даже при высоком уровне шума R &gt; 20 % и демонстрируют устойчивость к низкому и среднему уровням шума. Исследование выявило, что настройка веса физической функции потерь является одним из ключевым параметров для достижения оптимального баланса функциями потерь физических закономерностей и экспериментальных данных. Увеличение количества измерительных точек положительно влияет на точность при низком уровне шума. Увеличение количества измерительных точек при высоком уровне шума измерений снижает точность предсказаний модели. Научная новизна исследования заключается в предложении подхода к расчету строительных конструкций с использованием PINN, который интегрирует физические законы в процесс обучения. Полученные результаты подтверждают перспективность использования PINN для инженерных расчетов, особенно в условиях ограниченного объема данных.</p></abstract><trans-abstract xml:lang="en"><p>This article presents the development and analysis of a Physics-Informed Neural Network (PINN) model for calculating the deflection of a simply supported beam under uniformly distributed load. The training dataset was synthesized based on analytical principles of structural mechanics and included the following parameters: relative length of the measurement section l, number of measurement points N, and noise level R. The training dataset consisted of 1,296 rows describing random points within the beam span. In this study, 480 PINN models were trained to evaluate the impact of the weight of the physics-informed loss function, the number of measurements, and the noise level on prediction accuracy. The results demonstrated that PINN models achieve high accuracy (R2 ≥ 0.88) even with high noise levels (R &gt; 20 %) and exhibit robustness to low and moderate noise levels. The study identified that adjusting the weight of the physics-informed loss function is a key parameter for achieving an optimal balance between the loss functions of physical laws and experimental data. Increasing the number of measurement points positively influences accuracy at low noise levels. However, an increase in the number of measurement points under high noise levels reduces the prediction accuracy of the model. The scientific novelty of the study lies in proposing an approach for structural analysis using PINN, which integrates physical laws into the training process. The findings confirm the potential of using PINN for engineering calculations, particularly under limited data conditions.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>физически-информированные нейронные сети</kwd><kwd>строительная механика</kwd><kwd>ограниченный объем данных</kwd><kwd>искусственный интеллект</kwd><kwd>расчет балки</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Physics-Informed Neural Networks</kwd><kwd>structural mechanics</kwd><kwd>limited data</kwd><kwd>artificial intelligence</kwd><kwd>beam calculation</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Авторы искренне благодарят господина Цю Лимина, Президента компании Блютаун Леджу Констракшн Менеджмент Ко. Лтд., за предоставленную поддержку, включая обеспечение необходимыми ресурсами, административное содействие и помощь в установлении значимых контактов. Его неизменная поддержка науки и инноваций заслуживает глубочайшего уважения и высокой оценки, отражая преданность прогрессу и развитию строительной отрасли.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Szabó B.A., Babuška I. Finite Element Analysis: Method, Verification, and Validation. 2nd ed. Hoboken : Wiley, 2021. 374 p.</mixed-citation><mixed-citation xml:lang="en">Szabó B.A., Babuška I. Finite Element Analysis: Method, Verification, and Validation. 2nd ed. Hoboken, Wiley, 2021; 374.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Ereiz S., Duvnjak I., Jiménez-Alonso J.F. Review of finite element model updating methods for structural applications // Structures. 2022. Vol. 41. Pр. 684–723. 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