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Model Reduction and Fluctuation Response for Two-Timescale Systems.

機(jī)譯：兩時(shí)標(biāo)系統(tǒng)的模型歸約和波動(dòng)響應(yīng)。

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摘要

The purpose of this work is to study an application of the averaging method for the model reduction of chaotic two-timescale systems of ordinary differential equations. We focus on two practical implementations of the averaging method: first a simple implementation averaging with respect to a single invariant measure, then a second implementation which includes a linear response closure term derived from the fluctuation-dissipation theorem. Particular emphasis is placed on the ability of the reduced systems to capture the long-time statistics and ensemble perturbation response of the slow variables in the full system, which is not guaranteed by the averaging formalism. We present some theory in the general case regarding criteria for the similarity of the perturbation responses, then these methods are applied to a Lorenz 96 system for linear and higher-order coupling between slow and fast systems. From these numerical experiments we show that the addition of the linear response closure term greatly improves the reduced model's accuracy in capturing the dynamical and statistical behavior of the full system and could be useful in practice in the presence of computational constraints.
機(jī)譯：這項(xiàng)工作的目的是研究平均方法在常微分方程的混沌兩時(shí)標(biāo)系統(tǒng)模型降階中的應(yīng)用。我們關(guān)注平均方法的兩種實(shí)際實(shí)現(xiàn)：首先是對(duì)單個(gè)不變度量進(jìn)行平均的簡(jiǎn)單實(shí)現(xiàn)，然后是第二種實(shí)現(xiàn)，其中包括從波動(dòng)耗散定理得出的線性響應(yīng)閉合項(xiàng)。特別強(qiáng)調(diào)的是簡(jiǎn)化系統(tǒng)捕獲完整系統(tǒng)中慢變量的長(zhǎng)期統(tǒng)計(jì)數(shù)據(jù)和整體擾動(dòng)響應(yīng)的能力，而這并不是平均形式主義所能保證的。我們?cè)谝话闱闆r下介紹了一些有關(guān)擾動(dòng)響應(yīng)相似性準(zhǔn)則的理論，然后將這些方法應(yīng)用于Lorenz 96系統(tǒng)，以實(shí)現(xiàn)慢速系統(tǒng)和快速系統(tǒng)之間的線性和高階耦合。從這些數(shù)值實(shí)驗(yàn)中我們可以看出，線性響應(yīng)閉合項(xiàng)的增加極大地提高了簡(jiǎn)化模型在捕獲整個(gè)系統(tǒng)的動(dòng)態(tài)和統(tǒng)計(jì)行為方面的準(zhǔn)確性，并且在存在計(jì)算約束的情況下可能非常有用。

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  • 作者

    Kjerland, Marc Pierre.;

  • 作者單位

    University of Illinois at Chicago.;

  • 授予單位 University of Illinois at Chicago.;
  • 學(xué)科 Mathematics.;Theoretical physics.;Statistics.;Atmospheric sciences.
  • 學(xué)位 Ph.D.
  • 年度 2015
  • 頁(yè)碼 97 p.
  • 總頁(yè)數(shù) 97
  • 原文格式 PDF
  • 正文語(yǔ)種 eng
  • 中圖分類 遙感技術(shù);
  • 關(guān)鍵詞

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