{"paper":{"title":"Differentiable Hybrid Neural-CFD Modelling of Wall-Bounded Turbulence: Coupled Learning of Subgrid-Scale and Wall Closures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Jian-Xun Wang, Meng Wang, Xiantao Fan, Yi Liu","submitted_at":"2026-07-19T17:49:51Z","abstract_excerpt":"Wall-modelled large-eddy simulation (WMLES) treats the subgrid-scale (SGS) closure, wall closure and numerical discretization as independent components, although their effects are coupled through the same resolved field. We present a differentiable hybrid neural--CFD framework in which the SGS and wall closures are learned jointly, end-to-end, within a differentiable flow solver, using only low-order statistics as training targets. Each closure is a composed neural operator: a trainable neural network followed by a fixed differentiable layer that preserves the structure of its conventional cou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17357","kind":"arxiv","version":1},"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/2607.17357/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"}