{"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/reduced-order-model-for-fluid-flows-via","title":"Reduced-order Model for Fluid Flows via Neural Ordinary Differential Equations","arxiv_id":"2102.02248","date":"2021-02-03","proceeding":null,"authors":["Carlos J. G. Rojas","Andreas Dengel","Mateus Dias Ribeiro"],"abstract":"Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can decrease the computational burden of numerical solutions, while preserving the most important features of complex physical problems. In this paper, we use the proper orthogonal decomposition to reduce the dimensionality of the model and introduce a novel generative neural ODE (NODE) architecture to forecast the behavior of the temporal coefficients. With this methodology, we replace the classical Galerkin projection with an architecture characterized by the use of a continuous latent space. We exemplify the methodology on the dynamics of the Von Karman vortex street of the flow past a cylinder generated by a Large-eddy Simulation (LES)-based code. We compare the NODE methodology with an LSTM baseline to assess the extrapolation capabilities of the generative model and present some qualitative evaluations of the flow reconstructions.","url_abs":"https://arxiv.org/abs/2102.02248v1","url_pdf":"https://arxiv.org/pdf/2102.02248v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"reduced-order-model-for-fluid-flows-via","repo_url":"https://github.com/CarlosJose126/NeuralODE-ROM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2102.02248","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2102.02248"}},"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/CarlosJose126/NeuralODE-ROM","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":"3704cea53a9d6582","entry":"LatentOdeF","repo":"CarlosJose126/NeuralODE-ROM","repo_kind":"official","path":"VKS_node.py","file_url":"https://github.com/CarlosJose126/NeuralODE-ROM/blob/HEAD/VKS_node.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"3704cea53a9d6582"}},{"code_sha256_prefix":"5a9b90e8d2981ca2","entry":"normal_kl","repo":"CarlosJose126/NeuralODE-ROM","repo_kind":"official","path":"VKS_node.py","file_url":"https://github.com/CarlosJose126/NeuralODE-ROM/blob/HEAD/VKS_node.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"5a9b90e8d2981ca2"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}