{"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/enhancing-fourier-neural-operators-with-local","title":"Enhancing Fourier Neural Operators with Local Spatial Features","arxiv_id":"2503.17797","date":"2025-03-22","proceeding":null,"authors":["Chaoyu Liu","Davide Murari","Lihao Liu","Yangming Li","Chris Budd","Carola-Bibiane Schönlieb"],"abstract":"Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as an efficient approach for solving these PDE problems. By using parametrization in the frequency domain, FNOs can efficiently capture global patterns. However, this approach inherently overlooks the critical role of local spatial features, as frequency-domain parameterized convolutions primarily emphasize global interactions without encoding comprehensive localized spatial dependencies. Although several studies have attempted to address this limitation, their extracted Local Spatial Features (LSFs) remain insufficient, and computational efficiency is often compromised. To address this limitation, we introduce a convolutional neural network (CNN)-based feature pre-extractor to capture LSFs directly from input data, resulting in a hybrid architecture termed \\textit{Conv-FNO}. Furthermore, we introduce two novel resizing schemes to make our Conv-FNO resolution invariant. In this work, we focus on demonstrating the effectiveness of incorporating LSFs into FNOs by conducting both a theoretical analysis and extensive numerical experiments. Our findings show that this simple yet impactful modification enhances the representational capacity of FNOs and significantly improves performance on challenging PDE benchmarks.","url_abs":"https://arxiv.org/abs/2503.17797v2","url_pdf":"https://arxiv.org/pdf/2503.17797v2.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":"enhancing-fourier-neural-operators-with-local","repo_url":"https://github.com/neuraloperator/neuraloperator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"}],"methods":[{"method_slug":"focus","method_name":"Focus"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2503.17797","atlas_url":"https://app.syntology.ai/?focus=2503.17797","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2503.17797"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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/neuraloperator/neuraloperator","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{},"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":1,"samples":[{"code_sha256_prefix":"2041982f0cf2a6be","entry":"partialclass","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"2041982f0cf2a6be"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}