Parametric domain decomposition for accurate reduced order models: Applications of MP-LROM methodology
Parametric domain decomposition for accurate reduced order models: Applications of MP-LROM methodology
复制标题
精确降阶模型的参数域分解：MP-LROM 方法的应用
DOI：
10.1016/j.cam.2017.11.018
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发表时间：
2018
影响因子：
2.4
通讯作者：
Sandu, Adrian
中科院分区：
文献类型：
--
作者：
Stefanescu, Razvan;Moosavi, Azam;Sandu, Adrian
Moosavi等人最近提出的多变量局部降阶模型预测(MP-LROM)方法。(0000)，使用基于机器学习的回归方法来预测降阶模型的误差。这项研究考虑了MP-LROM的两个应用。首先，将误差模型与贪婪采样算法结合使用，生成具有重叠区域的一维参数区域的分解，使得相关的局部降阶模型满足规定的精度要求。一旦构造了参数区域分解，任何参数配置都属于(至少)其中一个分区；与该分区相关联的局部降阶模型在先验估计的精度水平内以给定的参数逼近全阶模型。参数域分解创建可用局部基、局部降阶和高保真模型的数据库，并确定任意参数配置的最准确解。接下来，使用该数据库来提高降阶模型的精度：(1)矩阵空间中约化基的拉格朗日插值法；(2)格拉斯曼流形切线空间中约化基的拉格朗日插值法；(3)在Gram-Schmidt正交化过程之后的约化基的串联；以及(4)高保真模型解的拉格朗日插值法。粘性Burgers模型的数值结果说明了MP-LROM法在改进参数降阶模型设计方面的潜力。
The multivariate predictions of local reduced-order-models (MP-LROM) methodology, recently proposed by the authors Moosavi et al. (0000), uses machine learning based regression methods to predict the errors of reduced-order models. This study considers two applications of MP-LROM. First, the error model is used in conjunction with a greedy sampling algorithm to generate decompositions of one dimensional parametric domains with overlapping regions, such that the associated local reduced-order models meet the prescribed accuracy requirements. Once a parametric domain decomposition is constructed, any parametric configuration belongs to (at least) one of the partitions; the local reduced-order model associated with that partition approximates the full order model at the given parameters within an accuracy level that is estimated a-priori. The parameter domain decomposition creates a database of the available local bases, local reduced-order, and high-fidelity models, and identifies the most accurate solutions for an arbitrary parametric configuration. Next, this database is used to enhance the accuracy of the reduced-order models using: (1) Lagrange interpolation of reduced bases in the matrix space; (2) Lagrange interpolation of reduced bases in the tangent space of the Grassmann manifold; (3) concatenation of reduced bases followed by a Gram–Schmidt orthogonalization process; and (4) Lagrange interpolation of high-fidelity model solutions. Numerical results with a viscous Burgers model illustrate the potential of the MP-LROM methodology to improve the design of parametric reduced-order models.
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DOI：
10.2514/6.2004-889
发表时间：
2003-11
期刊：
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影响因子：
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作者：
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通讯作者：
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DOI：
10.1002/nme.3327
发表时间：
2012-04-27
影响因子：
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影响因子：
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DOI：
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发表时间：
2006
期刊：
影响因子：
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