Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics

TL;DR

This paper compares Neural FEM and Neural Operator methods for solid mechanics, highlighting their differences in computational effort and accuracy through numerical experiments, and discusses their suitability for elastostatics applications.

Contribution

It provides a comparative analysis of Neural FEM and Neural Operator methods in elastostatics, focusing on training costs, accuracy, and practical application considerations.

Findings

Neural Operator methods require expensive training.

Neural Operator methods enable solving multiple problems with one model.

Accuracy of Neural Operator methods needs further research.

Abstract

Machine Learning methods belong to the group of most up-to-date approaches for solving partial differential equations. The current work investigates two classes, Neural FEM and Neural Operator Methods, for the use in elastostatics by means of numerical experiments. The Neural Operator methods require expensive training but then allow for solving multiple boundary value problems with the same Machine Learning model. Main differences between the two classes are the computational effort and accuracy. Especially the accuracy requires more research for practical applications.