Separable Physics-Informed Neural Networks for the solution of elasticity problems
This incremental improvement addresses computational challenges in simulating industrial-scale elasticity problems with complex geometries for engineers and researchers.
The authors tackled elasticity problems by proposing separable physics-informed neural networks (SPINN) with the deep energy method (DEM), achieving significantly higher convergence rate and accuracy compared to vanilla PINNs and SPINN based on PDEs, and enabling solutions on complex geometries where PINNs fail.
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.