  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.
