{"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/quantifying-model-form-uncertainty-in","title":"Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks","arxiv_id":"1807.02901","date":"2018-07-08","proceeding":null,"authors":["Nicholas Geneva","Nicholas Zabaras"],"abstract":"Data-driven methods for improving turbulence modeling in Reynolds-Averaged\nNavier-Stokes (RANS) simulations have gained significant interest in the\ncomputational fluid dynamics community. Modern machine learning algorithms have\nopened up a new area of black-box turbulence models allowing for the tuning of\nRANS simulations to increase their predictive accuracy. While several\ndata-driven turbulence models have been reported, the quantification of the\nuncertainties introduced has mostly been neglected. Uncertainty quantification\nfor such data-driven models is essential since their predictive capability\nrapidly declines as they are tested for flow physics that deviate from that in\nthe training data. In this work, we propose a novel data-driven framework that\nnot only improves RANS predictions but also provides probabilistic bounds for\nfluid quantities such as velocity and pressure. The uncertainties capture both\nmodel form uncertainty as well as epistemic uncertainty induced by the limited\ntraining data. An invariant Bayesian deep neural network is used to predict the\nanisotropic tensor component of the Reynolds stress. This model is trained\nusing Stein variational gradient decent algorithm. The computed uncertainty on\nthe Reynolds stress is propagated to the quantities of interest by vanilla\nMonte Carlo simulation. Results are presented for two test cases that differ\ngeometrically from the training flows at several different Reynolds numbers.\nThe prediction enhancement of the data-driven model is discussed as well as the\nassociated probabilistic bounds for flow properties of interest. Ultimately\nthis framework allows for a quantitative measurement of model confidence and\nuncertainty quantification for flows in which no high-fidelity observations or\nprior knowledge is available.","url_abs":"http://arxiv.org/abs/1807.02901v3","url_pdf":"http://arxiv.org/pdf/1807.02901v3.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":"quantifying-model-form-uncertainty-in","repo_url":"https://github.com/cics-nd/rans-uncertainty","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"form","task_name":"Form"},{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.02901","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1807.02901"}},"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/cics-nd/rans-uncertainty","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":1},"by_repo_kind":{"official":{"samples":1,"ran":0,"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":"65b3abaaab74f846","entry":"parameters_to_vector","repo":"cics-nd/rans-uncertainty","repo_kind":"official","path":"invar-nn/nn/nnUtils.py","file_url":"https://github.com/cics-nd/rans-uncertainty/blob/HEAD/invar-nn/nn/nnUtils.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":"65b3abaaab74f846"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}