This article is cited in 1 paper

Computer science

Separable physics-informed neural networks for solving elasticity problems

V. A. Eskin^ab, D. V. Davydov^ac, Yu. V. Gur'eva^ad, A. O. Malkhanov^a, M. E. Smorkalov<sup>ae

a</sup> Huawei Nizhny Novgorod Research Center, Nizhny Novgorod, Russia
^b National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
^c Mechanical Engineering Research Institute of RAS, Nizhny Novgorod
^d Huawei Technologies Co., Ltd.
^e Skolkovo Institute of Science and Technology, Moscow, Russia

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.

Key words: deep learning, physics-informed neural networks, partial differential equations, predictive modelling, computational physics.

UDC: 519.72

Received: 17.12.2024
Revised: 27.05.2025
Accepted: 20.06.2025

Language: English

DOI: 10.31857/S0044466925090107

 English version: Computational Mathematics and Mathematical Physics, 2025, 65:9, 2260–2275

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