{"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/on-the-locality-of-local-neural-operator-in","title":"On the locality of local neural operator in learning fluid dynamics","arxiv_id":"2312.09820","date":"2023-12-15","proceeding":null,"authors":["Ximeng Ye","Hongyu Li","Jingjie Huang","Guoliang Qin"],"abstract":"This paper launches a thorough discussion on the locality of local neural operator (LNO), which is the core that enables LNO great flexibility on varied computational domains in solving transient partial differential equations (PDEs). We investigate the locality of LNO by looking into its receptive field and receptive range, carrying a main concern about how the locality acts in LNO training and applications. In a large group of LNO training experiments for learning fluid dynamics, it is found that an initial receptive range compatible with the learning task is crucial for LNO to perform well. On the one hand, an over-small receptive range is fatal and usually leads LNO to numerical oscillation; on the other hand, an over-large receptive range hinders LNO from achieving the best accuracy. We deem rules found in this paper general when applying LNO to learn and solve transient PDEs in diverse fields. Practical examples of applying the pre-trained LNOs in flow prediction are presented to confirm the findings further. Overall, with the architecture properly designed with a compatible receptive range, the pre-trained LNO shows commendable accuracy and efficiency in solving practical cases.","url_abs":"https://arxiv.org/abs/2312.09820v1","url_pdf":"https://arxiv.org/pdf/2312.09820v1.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":"on-the-locality-of-local-neural-operator-in","repo_url":"https://github.com/pphub-hy/torch-lno-compressible-fluid-dynamics","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2312.09820","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2312.09820"}},"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/pphub-hy/torch-lno-compressible-fluid-dynamics","reach":{"status":"ok","spdx":"Apache-2.0"}}],"summary":{"ran":3},"by_repo_kind":{"official":{"samples":3,"ran":3,"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":"55d32fc1f5e216cc","entry":"generte_boundary_filters_2D","repo":"pphub-hy/torch-lno-compressible-fluid-dynamics","repo_kind":"official","path":"Train_Validation/lib/utils.py","file_url":"https://github.com/pphub-hy/torch-lno-compressible-fluid-dynamics/blob/HEAD/Train_Validation/lib/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"55d32fc1f5e216cc"}},{"code_sha256_prefix":"3ac88294779c2aa0","entry":"generte_legendre_filters_1D","repo":"pphub-hy/torch-lno-compressible-fluid-dynamics","repo_kind":"official","path":"Train_Validation/lib/utils.py","file_url":"https://github.com/pphub-hy/torch-lno-compressible-fluid-dynamics/blob/HEAD/Train_Validation/lib/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"3ac88294779c2aa0"}},{"code_sha256_prefix":"eac9cf0cc68797f1","entry":"generte_legendre_filters_2D","repo":"pphub-hy/torch-lno-compressible-fluid-dynamics","repo_kind":"official","path":"Application/lib/utils.py","file_url":"https://github.com/pphub-hy/torch-lno-compressible-fluid-dynamics/blob/HEAD/Application/lib/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"eac9cf0cc68797f1"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}