РАЗДЕЛЯЕМЫЕ ФИЗИЧЕСКИ-ОБУСЛОВЛЕННЫЕ НЕЙРОННЫЕ СЕТИ ДЛЯ РЕШЕНИЯ ЗАДАЧ УПРУГОСТИ

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Аннотация

Представлен метод решения задач упругости, основанный на разделяемых физически-обусловленных нейронных сетях (SPINN), в сочетании с методом глубокой энергии (DEM). Были проведены численные эксперименты для ряда задач, показавшие, что этот метод обладает значительно более высокой скоростью сходимости и точностью, чем обычные физически-обусловленные нейронные сети (PINN) и даже SPINN, основанные на системе дифференциальных уравнений в частных производных (PDE). Кроме того, используя SPINN в рамках подхода DEM, можно решать задачи линейной теории упругости на сложных геометриях, что недостижимо с помощью PINN в рамках дифференциальных уравнений в частных производных. Рассмотренные задачи очень близки к промышленным задачам с точки зрения геометрии, нагрузки и параметров материала. Библ. 61. Фиг. 6. Табл. 8.

Об авторах

В. А Еськин

Нижегородский государственный университет; Huawei Nizhny Novgorod Research Center

Автор, ответственный за переписку.
Email: vasiliy.eskin@gmail.com
Нижний Новгород, Россия

Д. В Давыдов

Институт проблем машиностроения Российской академии наук; Huawei Nizhny Novgorod Research Center

Email: davidovdan274@yandex.ru
Нижний Новгород, Россия; Нижний Новгород, Россия

Ю. В Гурьева

Huawei Nizhny Novgorod Research Center

Email: gureva-yulya@list.ru
Нижний Новгород, Россия

А. О Мальханов

Huawei Nizhny Novgorod Research Center

Email: alexey.malkhanov@gmail.com
Нижний Новгород, Россия

М. Е Сморкалов

Huawei Nizhny Novgorod Research Center; Сколковский институт науки и технологий

Email: smorkalovne@gmail.com
Нижний Новгород, Россия; Москва, Россия

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