2023/07/04 by Stefan Hildebrand, Hildebrand, Stefan, Sandra Klinge +1 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Finance #Magnetic Properties and Applications #Materials Science (cond-mat.mtrl-sci) #Model Reduction and Neural Networks #Neural and Evolutionary Computing (cs.NE) #Non-Destructive Testing Techniques #Numerical Analysis (math.NA) #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2307.02494
openalex publication_date 2023/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.