Separable Physics-Informed Neural Networks for the solution of elasticity problems

TL;DR

This paper introduces a separable physics-informed neural network (SPINN) combined with the deep energy method (DEM) to efficiently solve elasticity problems, achieving higher accuracy and convergence than traditional PINNs, especially on complex geometries.

Contribution

The paper presents a novel SPINN approach integrated with DEM, enabling accurate elasticity solutions on complex geometries where PINNs struggle.

Findings

SPINN with DEM outperforms vanilla PINNs in convergence and accuracy.

The method effectively handles complex geometries in elasticity problems.

Applicable to industrial-like problems with realistic geometries and loadings.

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.