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.

翻译：机器学习方法属于求解偏微分方程的最新方法之一。本研究通过数值实验，探讨了两类方法——神经有限元法（Neural FEM）和神经算子方法（Neural Operator Methods）在弹性静力学中的应用。神经算子方法需要高昂的训练成本，但随后能够使用同一机器学习模型求解多个边值问题。这两类方法的主要区别在于计算工作量与精度。特别是精度问题，在面向实际应用时尚需进一步研究。