{"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/operator-learning-with-neural-fields-tackling","title":"Operator Learning with Neural Fields: Tackling PDEs on General Geometries","arxiv_id":"2306.07266","date":"2023-06-12","proceeding":"NeurIPS 2023 11","authors":["Louis Serrano","Lise Le Boudec","Armand Kassaï Koupaï","Thomas X Wang","Yuan Yin","Jean-Noël Vittaut","Patrick Gallinari"],"abstract":"Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and inverse problems like geometric design. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.","url_abs":"https://arxiv.org/abs/2306.07266v2","url_pdf":"https://arxiv.org/pdf/2306.07266v2.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":"operator-learning-with-neural-fields-tackling","repo_url":"https://github.com/louisserrano/coral","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"operator-learning","task_name":"Operator learning"},{"task_slug":"spatio-temporal-forecasting","task_name":"Spatio-Temporal Forecasting"}],"methods":[{"method_slug":"coral","method_name":"CORAL"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2306.07266","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2306.07266"}},"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/louisserrano/coral","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":1,"unverified":5},"by_repo_kind":{"official":{"samples":6,"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":"30f9a317c56b5420","entry":"per_element_nll_fn","repo":"louisserrano/coral","repo_kind":"official","path":"coral/losses.py","file_url":"https://github.com/louisserrano/coral/blob/HEAD/coral/losses.py","link_basis":"plan_row","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"30f9a317c56b5420"}},{"code_sha256_prefix":"f06696c3d9b07011","entry":"AR_forward","repo":"louisserrano/coral","repo_kind":"official","path":"baseline/deeponet/coral/deeponet_model.py","file_url":"https://github.com/louisserrano/coral/blob/HEAD/baseline/deeponet/coral/deeponet_model.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":"f06696c3d9b07011"}},{"code_sha256_prefix":"e8abeb49bc4d48ae","entry":"IntegratedPositionalEncoding","repo":"louisserrano/coral","repo_kind":"official","path":"coral/mfn.py","file_url":"https://github.com/louisserrano/coral/blob/HEAD/coral/mfn.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":"e8abeb49bc4d48ae"}},{"code_sha256_prefix":"cdee26ce4b13d516","entry":"batch_multi_scale_fn","repo":"louisserrano/coral","repo_kind":"official","path":"coral/losses.py","file_url":"https://github.com/louisserrano/coral/blob/HEAD/coral/losses.py","link_basis":"plan_row","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":"cdee26ce4b13d516"}},{"code_sha256_prefix":"0b06beefea39b45f","entry":"layer_factory","repo":"louisserrano/coral","repo_kind":"official","path":"coral/mfn.py","file_url":"https://github.com/louisserrano/coral/blob/HEAD/coral/mfn.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":"0b06beefea39b45f"}},{"code_sha256_prefix":"fde22d55da472aed","entry":"per_element_multi_scale_fn","repo":"louisserrano/coral","repo_kind":"official","path":"coral/losses.py","file_url":"https://github.com/louisserrano/coral/blob/HEAD/coral/losses.py","link_basis":"plan_row","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":"fde22d55da472aed"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}