{"paper":{"title":"Accelerating Galerkin Reduced-Order Models for Turbulent Flows with Tensor Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"physics.flu-dyn","authors_text":"(2) University of Illinois Urbana-Champaign), Edgar Solomonik (2) ((1) Virginia Tech, Paul Fischer (2), Ping-Hsuan Tsai (1)","submitted_at":"2023-11-07T03:47:05Z","abstract_excerpt":"Galerkin-based reduced-order models (G-ROMs) offer efficient and accurate approximations for laminar flows but require hundreds to thousands of modes $N$ to capture the complex dynamics of turbulent flows. This makes standard G-ROMs computationally expensive due to the third-order advection tensor contraction, requiring the storage of $N^3$ entries and the computation of $2N^3$ operations per timestep. As a result, such ROMs are impractical for realistic applications like turbulent flow control. In this work, we consider problems that demand large $N$ values for accurate G-ROMs and propose a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03694","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.03694/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}