SEPARABLE PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING ELASTICITY PROBLEMS

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Abstract

Abstract –A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing that this method has a significantly higher convergence rate and accuracy than the vanilla physics-informed neural networks (PINN) and even SPINN based on a system of partial differential equations (PDEs). In addition, using the SPINN in the framework of DEM approach it is possible to solve problems of the linear theory of elasticity on complex geometries, which is unachievable with the help of PINNs in frames of partial differential equations. Considered problems are very close to the industrial problems in terms of geometry, loading, and material parameters. Bibl. 61. Fig. 6. Tabl. 8.

About the authors

V. A Es'kin

University of Nizhny Novgorod; Huawei Nizhny Novgorod Research Center

Author for correspondence.
Email: vasiliy.eskin@gmail.com
Nizhny Novgorod, Russia; Nizhny Novgorod, Russia

D. V Davydov

Mechanical Engineering Research Institute of Russian Academy of Sciences; Huawei Nizhny Novgorod Research Center

Email: davidovdan274@yandex.ru
Nizhny Novgorod, Russia; Nizhny Novgorod, Russia

J. V Gur'eva

Huawei Nizhny Novgorod Research Center

Email: gureva-yulya@list.ru
Nizhny Novgorod, Russia

A. O Malkhanov

Huawei Nizhny Novgorod Research Center

Email: alexey.malkhanov@gmail.com
Nizhny Novgorod, Russia

M. E Smorkalov

Huawei Nizhny Novgorod Research Center; Skolkovo Institute of Science and Technology

Email: smorkalovne@gmail.com
Nizhny Novgorod, Russia; Moscow, Russia

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