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

arXiv: https://arxiv.org/abs/2307.02494 · HTML: https://mlsanity.com/paper/2307.02494/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2023.

## Built on by (most cited first, 3 of 3)

- [Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations](https://mlsanity.com/paper/2401.02363/) (2024)
- [Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks](https://mlsanity.com/paper/2403.01776/) (2024)
- [FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel](https://mlsanity.com/paper/2610.04212/) (2026)

## Abstract (arXiv)

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.