Экстраполяция решения уравнения Дуффинга при помощи RBF-сети

Аннотация

В статье рассматривается проблема аппроксимации решения задачи Коши для обыкновенного дифференциального уравнения второго порядка. Схема аппроксимации основана на разложении решения по Тейлору с остаточным членом в форме Лагранжа. Остаточный член ищется в виде выхода нейронной сети с радиально-базисными функциями (RBF-сети). Представлен алгоритм обучения (выбора оптимальных параметров) RBF-сети. На примере решения задачи Коши для нелинейного дифференциального уравнения второго порядка – осциллятора Дуффинга исследовано влияние различных радиально-базисных функций на качество интерполяции и экстраполяции решения уравнения Дуффинга.

Сведения об авторах

Tatyana Valerievna Lazovskaya, Санкт-Петербургский политехнический университет Петра Великого

старший преподаватель кафедры высшей математики физико-механического института

Galina Fedorovna Malykhina, Санкт-Петербургский политехнический университет Петра Великого

профессор высшей школы киберфизических систем и управления института компьютерных наук и технологий, доктор технических наук, доцент

Dmitry Maksimovich Pashkovsky, Санкт-Петербургский политехнический университет Петра Великого

студент физико-механического института

Dmitry Albertovich Tarkhov, Санкт-Петербургский политехнический университет Петра Великого

профессор кафедры высшей математики физико-механического института, доктор технических наук, доцент

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Опубликована
2021-12-20
Как цитировать
LAZOVSKAYA, Tatyana Valerievna et al. Экстраполяция решения уравнения Дуффинга при помощи RBF-сети. Современные информационные технологии и ИТ-образование, [S.l.], v. 17, n. 4, p. 998-1006, dec. 2021. ISSN 2411-1473. Доступно на: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/775>. Дата доступа: 09 dec. 2022 doi: https://doi.org/10.25559/SITITO.17.202104.998-1006.
Раздел
Научное программное обеспечение в образовании и науке

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