arXiv:2510.02982physics.flu-dyncs.LG2025-10被引 2

用在线生成的高精度数据训练湍流模型,提升泛化能力。

oRANS: Online optimisation of RANS machine learning models with embedded DNS data generation

  • 在RANS域内嵌入DNS,实时生成训练数据
  • 在线优化使模型在多种雷诺数下表现更优
  • 适合需要跨工况泛化的流体模拟研究者

深度学习在加速和提升流体模拟精度方面展现潜力,但受限于高保真训练数据稀缺——这类数据生成成本高,且仅适用于有限流态。传统离线训练的湍流模型易过拟合,难以推广至新工况。本文提出一种在线优化框架,用于基于深度学习的雷诺平均纳维-斯托克斯(RANS)模型闭合。通过在RANS域中嵌入直接数值模拟(DNS)子域,动态生成训练数据:RANS解为DNS提供边界条件,而DNS则输出平均速度与湍流统计量,用于实时更新深度学习闭合模型。该反馈机制使模型能适应嵌入式DNS目标流场,避免依赖预存数据集,显著提升外分布性能。实验针对随机强迫的伯格斯方程及雷诺数分别为 $Re_τ=180$、$270$、$395$、$590$ 的湍流通道流,嵌入域长度比 $1\leq L_0/L\leq 8$。在线优化模型显著优于离线训练与文献标定模型,仅需较小的DNS子域即可实现高精度训练。性能下降主要发生在边界条件污染严重或域长不足以捕捉低波数模态时。该框架为物理信息驱动的机器学习闭合提供了可扩展路径,实现无需大规模预存数据集的自适应降阶模型。

原文摘要 · Abstract (English)

Deep learning (DL) has demonstrated promise for accelerating and enhancing the accuracy of flow physics simulations, but progress is constrained by the scarcity of high-fidelity training data, which is costly to generate and inherently limited to a small set of flow conditions. Consequently, closures trained in the conventional offline paradigm tend to overfit and fail to generalise to new regimes. We introduce an online optimisation framework for DL-based Reynolds-averaged Navier--Stokes (RANS) closures which seeks to address the challenge of limited high-fidelity datasets. Training data is dynamically generated by embedding a direct numerical simulation (DNS) within a subdomain of the RANS domain. The RANS solution supplies boundary conditions to the DNS, while the DNS provides mean velocity and turbulence statistics that are used to update a DL closure model during the simulation. This feedback loop enables the closure to adapt to the embedded DNS target flow, avoiding reliance on precomputed datasets and improving out-of-distribution performance. The approach is demonstrated for the stochastically forced Burgers equation and for turbulent channel flow at $Re_τ=180$, $270$, $395$ and $590$ with varying embedded domain lengths $1\leq L_0/L\leq 8$. Online-optimised RANS models significantly outperform both offline-trained and literature-calibrated closures, with accurate training achieved using modest DNS subdomains. Performance degrades primarily when boundary-condition contamination dominates or when domains are too short to capture low-wavenumber modes. This framework provides a scalable route to physics-informed machine learning closures, enabling data-adaptive reduced-order models that generalise across flow regimes without requiring large precomputed training datasets.

湍流模拟深度学习在线学习流体建模

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