{"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/multiscale-neural-operators-for-solving-time","title":"Multiscale Neural Operators for Solving Time-Independent PDEs","arxiv_id":"2311.05964","date":"2023-11-10","proceeding":null,"authors":["Winfried Ripken","Lisa Coiffard","Felix Pieper","Sebastian Dziadzio"],"abstract":"Time-independent Partial Differential Equations (PDEs) on large meshes pose significant challenges for data-driven neural PDE solvers. We introduce a novel graph rewiring technique to tackle some of these challenges, such as aggregating information across scales and on irregular meshes. Our proposed approach bridges distant nodes, enhancing the global interaction capabilities of GNNs. Our experiments on three datasets reveal that GNN-based methods set new performance standards for time-independent PDEs on irregular meshes. Finally, we show that our graph rewiring strategy boosts the performance of baseline methods, achieving state-of-the-art results in one of the tasks.","url_abs":"https://arxiv.org/abs/2311.05964v1","url_pdf":"https://arxiv.org/pdf/2311.05964v1.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":"multiscale-neural-operators-for-solving-time","repo_url":"https://github.com/merantix-momentum/multiscale-pde-operators","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2311.05964","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2311.05964"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/merantix-momentum/multiscale-pde-operators","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":1,"unverified":1},"by_repo_kind":{"official":{"samples":2,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"eeae844c0b81c9f3","entry":"decompose_graph","repo":"merantix-momentum/multiscale-pde-operators","repo_kind":"official","path":"multiscale_operator/operators/helpers/utils.py","file_url":"https://github.com/merantix-momentum/multiscale-pde-operators/blob/HEAD/multiscale_operator/operators/helpers/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"eeae844c0b81c9f3"}},{"code_sha256_prefix":"aa40f077e97aadd9","entry":"copy_geometric_data","repo":"merantix-momentum/multiscale-pde-operators","repo_kind":"official","path":"multiscale_operator/operators/helpers/utils.py","file_url":"https://github.com/merantix-momentum/multiscale-pde-operators/blob/HEAD/multiscale_operator/operators/helpers/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"aa40f077e97aadd9"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}