{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/harnessing-scale-and-physics-a-multi-graph","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","arxiv_id":"2411.15178","date":"2024-11-18","proceeding":null,"authors":["Zhihao LI","Haoze Song","Di Xiao","Zhilu Lai","Wei Wang"],"abstract":"Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the \\textbf{AMG} method, a \\textbf{M}ulti-\\textbf{G}raph neural operator approach designed for efficiently solving PDEs on \\textbf{A}rbitrary geometries. AMG leverages advanced graph-based techniques and dynamic attention mechanisms within a novel GraphFormer architecture, enabling precise management of diverse spatial domains and complex data interdependencies. By constructing multi-scale graphs to handle variable feature frequencies and a physics graph to encapsulate inherent physical properties, AMG significantly outperforms previous methods, which are typically limited to uniform grids. We present a comprehensive evaluation of AMG across six benchmarks, demonstrating its consistent superiority over existing state-of-the-art models. Our findings highlight the transformative potential of tailored graph neural operators in surmounting the challenges faced by conventional PDE solvers. Our code and datasets are available on \\url{https://github.com/lizhihao2022/AMG}.","url_abs":"https://arxiv.org/abs/2411.15178v2","url_pdf":"https://arxiv.org/pdf/2411.15178v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"harnessing-scale-and-physics-a-multi-graph","repo_url":"https://github.com/lizhihao2022/amg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"management","task_name":"Management"}],"methods":[{"method_slug":"attention","method_name":"Attention"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[{"slug":"cylinderflow","name":"CylinderFlow","full_name":"CylinderFlow with dynamic grid"},{"slug":"poisson-equation","name":"Poisson Equation","full_name":"Poisson Equation with unstructured grid"}],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2411.15178","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}