Separable Physics-Informed Neural Networks for the solution of
  elasticity problems
Vasiliy A. Es'kin Danil V. Davydov Julia V. Gur'eva Alexey O. Malkhanov Mikhail E. Smorkalov
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.