2024/05/31 by Jens Decke, Decke, Jens, Olaf Wünsch +5
Computer Science · Engineering · #Computational Engineering #Computational Geometry and Mesh Generation #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Finance #Graph Theory and Algorithms #Machine Learning (cs.LG) #Manufacturing Process and Optimization #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2406.00081
openalex publication_date 2024/05/31 · openalex created_date 2024/06/06 · openalex updated_date 2026/07/28
This article investigates the application of computer vision and graph-based models in solving mesh-based partial differential equations within high-performance computing environments. Focusing on structured, graded structured, and unstructured meshes, the study compares the performance and computational efficiency of three computer vision-based models against three graph-based models across three data\-sets. The research aims to identify the most suitable models for different mesh topographies, particularly highlighting the exploration of graded meshes, a less studied area. Results demonstrate that computer vision-based models, notably U-Net, outperform the graph models in prediction performance and efficiency in two (structured and graded) out of three mesh topographies. The study also reveals the unexpected effectiveness of computer vision-based models in handling unstructured meshes, suggesting a potential shift in methodological approaches for data-driven partial differential equation learning. The article underscores deep learning as a viable and potentially sustainable way to enhance traditional high-performance computing methods, advocating for informed model selection based on the topography of the mesh.