Neural FEM与Neural Operator方法在固体力学应用中的比较
Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics
AI总结：
本文通过数值实验比较了Neural FEM与Neural Operator方法在弹性静力学中的应用，发现两者在计算量和精度上存在主要差异，且精度在实际应用中仍需进一步研究。
摘要：
机器学习方法属于求解偏微分方程的最前沿方法。当前工作通过数值实验研究了两类方法，即Neural FEM和Neural Operator方法，在弹性静力学中的应用。Neural Operator方法需要昂贵的训练，但随后允许使用同一机器学习模型求解多个边值问题。两类方法之间的主要差异在于计算量和精度。特别是精度在实际应用中需要更多研究。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
