{"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/finitenet-a-fully-convolutional-lstm-network","title":"FiniteNet: A Fully Convolutional LSTM Network Architecture for Time-Dependent Partial Differential Equations","arxiv_id":"2002.03014","date":"2020-02-07","proceeding":null,"authors":["Ben Stevens","Tim Colonius"],"abstract":"In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of PDEs. The neural network serves to enhance finite-difference and finite-volume methods (FDM/FVM) that are commonly used to solve PDEs, allowing us to maintain guarantees on the order of convergence of our method. We train the network on simulation data, and show that our network can reduce error by a factor of 2 to 3 compared to the baseline algorithms. We demonstrate our method on three PDEs that each feature qualitatively different dynamics. We look at the linear advection equation, which propagates its initial conditions at a constant speed, the inviscid Burgers' equation, which develops shockwaves, and the Kuramoto-Sivashinsky (KS) equation, which is chaotic.","url_abs":"https://arxiv.org/abs/2002.03014v1","url_pdf":"https://arxiv.org/pdf/2002.03014v1.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":"finitenet-a-fully-convolutional-lstm-network","repo_url":"https://github.com/FiniteNetICML2020Code/FiniteNet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"lstm","method_name":"LSTM"},{"method_slug":"sigmoid-activation","method_name":"Sigmoid Activation"},{"method_slug":"tanh-activation","method_name":"Tanh Activation"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.03014","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2002.03014"}},"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/FiniteNetICML2020Code/FiniteNet","reach":null}],"summary":{"ran":1,"ran_honours":1},"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":2,"samples":[{"code_sha256_prefix":"c5fe5d2d07f2f0c6","entry":"Model","repo":"FiniteNetICML2020Code/FiniteNet","repo_kind":"official","path":"train_KSNet.py","file_url":"https://github.com/FiniteNetICML2020Code/FiniteNet/blob/HEAD/train_KSNet.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"c5fe5d2d07f2f0c6"}},{"code_sha256_prefix":"f9080e1a05f18edb","entry":"reshKS","repo":"FiniteNetICML2020Code/FiniteNet","repo_kind":"official","path":"train_KSNet.py","file_url":"https://github.com/FiniteNetICML2020Code/FiniteNet/blob/HEAD/train_KSNet.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f9080e1a05f18edb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}