{"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/learning-green-s-functions-of-linear-reaction","title":"Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver","arxiv_id":"2105.11045","date":"2021-05-23","proceeding":null,"authors":["Yuankai Teng","XiaoPing Zhang","Zhu Wang","Lili Ju"],"abstract":"Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional numerical methods have been developed and widely used for their solutions. Inspired by rapidly growing impact of deep learning on scientific and engineering research, in this paper we propose a novel neural network, GF-Net, for learning the Green's functions of linear reaction-diffusion equations in an unsupervised fashion. The proposed method overcomes the challenges for finding the Green's functions of the equations on arbitrary domains by utilizing physics-informed approach and the symmetry of the Green's function. As a consequence, it particularly leads to an efficient way for solving the target equations under different boundary conditions and sources. We also demonstrate the effectiveness of the proposed approach by experiments in square, annular and L-shape domains.","url_abs":"https://arxiv.org/abs/2105.11045v2","url_pdf":"https://arxiv.org/pdf/2105.11045v2.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":"learning-green-s-functions-of-linear-reaction","repo_url":"https://github.com/sloooWTYK/GF-Net","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2105.11045","atlas_url":"https://app.syntology.ai/?focus=2105.11045","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2105.11045"}},"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/sloooWTYK/GF-Net","reach":null}],"summary":{"ran_fixture":2},"by_repo_kind":{"official":{"samples":2,"ran":2,"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":"45ef69f7d2715e38","entry":"calc_area","repo":"sloooWTYK/GF-Net","repo_kind":"official","path":"GreenFormula.py","file_url":"https://github.com/sloooWTYK/GF-Net/blob/HEAD/GreenFormula.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"45ef69f7d2715e38"}},{"code_sha256_prefix":"e466bec4001dfdc7","entry":"in_subdomain","repo":"sloooWTYK/GF-Net","repo_kind":"official","path":"GreenFormula.py","file_url":"https://github.com/sloooWTYK/GF-Net/blob/HEAD/GreenFormula.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e466bec4001dfdc7"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}