Subgrid Stress Modelling with Multi-dimensional State Space Sequence Models

[2511.10910] Subgrid Stress Modelling with Multi-dimensional State Space Sequence Models Skip to main content Search Submit Donate Log in Physics > Fluid Dynamics arXiv:2511.10910 (physics) [Submitted on 14 Nov 2025 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Subgrid Stress Modelling with Multi-dimensional State Space Sequence Models Authors: Andy Wu , Sanjiva K. Lele View PDF HTML (experimental) Abstract: Large Eddy Simulations (LES) are becoming increasingly viable due to the growth in computational power the last few decades, and subgrid stress modelling plays a large role in the accuracy of LES. A new class of neural network models, S4 and S4ND models, allow for learning a continuous representation of the discrete dataset, which facilitates a principled approach to incorporating grid dependence in neural network subgrid stress modelling. A S4ND Unet neural network architecture is proposed and trained on both forced Homogeneous Isotropic Turbulence (HIT) and channel flow, where a priori, it is shown to generalize to grid spacings that are coarser than the training set grid spacings, while simpler artificial neural network (ANN) models fail. A posteriori tests on both forced HIT and channel flow indicate that the S4ND model is more accurate than traditional models and ANN-based models on grid sizes that are in the training set. The S4ND model is also able to generalize to grid sizes that are coarser than the training set a posteriori, and is more accurate than many traditional and neural network subgrid stress models. Finally, the proposed model is also evaluated on flows at increasing Reynolds numbers, where it is seen that the proposed neural network remains stable even at a Reynolds number that is 500,000 times that seen in the training set. Subjects: Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2511.10910 [physics.flu-dyn] (or arXiv:2511.10910v2 [physics.flu-dyn] for this version) https://doi.org/10.48550/arXiv.2511.10910 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1017/jfm.2026.11929 Focus to learn more DOI(s) linking to related resources Submission history From: Andy Wu [ view email ] [v1] Fri, 14 Nov 2025 02:45:25 UTC (4,009 KB) [v2] Fri, 28 Aug 2026 05:00:16 UTC (4,541 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: physics.flu-dyn < prev | next > new | recent | 2025-11 Change to browse by: physics References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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