{"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-modeling-of-advection-dominated","title":"Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders","arxiv_id":"2002.00470","date":"2020-02-02","proceeding":null,"authors":["Romit Maulik","Bethany Lusch","Prasanna Balaprakash"],"abstract":"A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that an encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent-space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD Galerkin technique.","url_abs":"https://arxiv.org/abs/2002.00470v2","url_pdf":"https://arxiv.org/pdf/2002.00470v2.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-modeling-of-advection-dominated","repo_url":"https://github.com/Romit-Maulik/CAE_LSTM_ROMS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.00470","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2002.00470"}},"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/Romit-Maulik/CAE_LSTM_ROMS","reach":null}],"summary":{"ran_fixture":1},"by_repo_kind":{"official":{"samples":1,"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":1,"samples":[{"code_sha256_prefix":"3cd467aad1a57cfb","entry":"galerkin_projection","repo":"Romit-Maulik/CAE_LSTM_ROMS","repo_kind":"official","path":"Burgers_Equations/POD_GP/GP.py","file_url":"https://github.com/Romit-Maulik/CAE_LSTM_ROMS/blob/HEAD/Burgers_Equations/POD_GP/GP.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"3cd467aad1a57cfb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}