Yifei Guan, Pedram Hassanzadeh, Tapio Schneider, Oliver Dunbar, Daniel Zhengyu Huang, Jinlong Wu, Ignacio Lopez-Gomez
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Only a small training dataset is needed to\ncalculate the DNS spectra (i.e., the approach is {data-efficient}). We find the\noptimized parameter(s) of each closure to be constant across broad flow regimes\nthat differ in dominant length scales, eddy/jet structures, and dynamics,\nsuggesting that these closures are {generalizable}. In a-posteriori tests based\non the enstrophy spectra and probability density functions (PDFs) of vorticity,\nLES with optimized closures outperform the baselines (LES with standard Smag,\ndynamic Smag or Leith), particularly at the tails of the PDFs (extreme events).\nIn a-priori tests, the optimized JH significantly outperforms the baselines and\noptimized Smag and Leith in terms of interscale enstrophy and energy transfers\n(still, optimized Smag noticeably outperforms standard Smag). The results show\nthe promise of combining advances in physics-based modeling (e.g., JH) and\ndata-driven modeling (e.g., {online} learning with EKI) to develop\ndata-efficient frameworks for accurate, interpretable, and generalizable\nclosures.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Online learning of eddy-viscosity and backscattering closures for geophysical turbulence using ensemble Kalman inversion\",\"authors\":\"Yifei Guan, Pedram Hassanzadeh, Tapio Schneider, Oliver Dunbar, Daniel Zhengyu Huang, Jinlong Wu, Ignacio Lopez-Gomez\",\"doi\":\"arxiv-2409.04985\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Different approaches to using data-driven methods for subgrid-scale closure\\nmodeling have emerged recently. 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引用次数: 0
摘要
最近出现了不同的使用数据驱动方法进行亚网格尺度闭合建模的方法。这些方法大多对数据要求较高,缺乏可解释性和分布外概括性。在这里,我们使用在线学习来解决著名的基于物理的大尺度涡旋模拟(LES)闭合模型的参数不确定性问题:Smagorinsky(Smag)和 Leitheddy-粘度模型(1 个自由参数)以及 Jansen-Held (JH)反向散射模型(2 个自由参数)。针对 8 种二维地球物理扰动情况,利用集合卡尔曼反演(EKI)估算出最佳参数,从而使 LES 的能谱与直接数值模拟(DNS)的能谱相匹配。计算 DNS 能谱只需要少量的训练数据集(即该方法{数据效率高})。我们发现每个闭合的优化参数在不同的流态下都是恒定的,而这些流态在主要长度尺度、涡/射流结构和动力学方面都有所不同,这表明这些闭合是{可通用的}。在基于涡度的熵谱和概率密度函数(PDF)的后验中,采用优化闭合的 LES 优于基线(采用标准 Smag、动态 Smag 或 Leith 的 LES),尤其是在 PDF 的尾部(极端事件)。在先验测试中,优化 JH 在尺度间熵和能量传递方面明显优于基线、优化 Smag 和 Leith(但优化 Smag 仍明显优于标准 Smag)。这些结果表明,将基于物理的建模(如 JH)和数据驱动的建模(如使用 EKI 的{在线}学习)的进步结合起来,为准确、可解释和可推广的信息披露开发数据高效的框架是大有可为的。
Online learning of eddy-viscosity and backscattering closures for geophysical turbulence using ensemble Kalman inversion
Different approaches to using data-driven methods for subgrid-scale closure
modeling have emerged recently. Most of these approaches are data-hungry, and
lack interpretability and out-of-distribution generalizability. Here, we use
{online} learning to address parametric uncertainty of well-known physics-based
large-eddy simulation (LES) closures: the Smagorinsky (Smag) and Leith
eddy-viscosity models (1 free parameter) and the Jansen-Held (JH)
backscattering model (2 free parameters). For 8 cases of 2D geophysical
turbulence, optimal parameters are estimated, using ensemble Kalman inversion
(EKI), such that for each case, the LES' energy spectrum matches that of direct
numerical simulation (DNS). Only a small training dataset is needed to
calculate the DNS spectra (i.e., the approach is {data-efficient}). We find the
optimized parameter(s) of each closure to be constant across broad flow regimes
that differ in dominant length scales, eddy/jet structures, and dynamics,
suggesting that these closures are {generalizable}. In a-posteriori tests based
on the enstrophy spectra and probability density functions (PDFs) of vorticity,
LES with optimized closures outperform the baselines (LES with standard Smag,
dynamic Smag or Leith), particularly at the tails of the PDFs (extreme events).
In a-priori tests, the optimized JH significantly outperforms the baselines and
optimized Smag and Leith in terms of interscale enstrophy and energy transfers
(still, optimized Smag noticeably outperforms standard Smag). The results show
the promise of combining advances in physics-based modeling (e.g., JH) and
data-driven modeling (e.g., {online} learning with EKI) to develop
data-efficient frameworks for accurate, interpretable, and generalizable
closures.