A Training Set Subsampling Strategy for the Reduced Basis Method
A Training Set Subsampling Strategy for the Reduced Basis Method
复制标题
降基法的训练集二次抽样策略
DOI：
10.1007/s10915-021-01665-y
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发表时间：
2021
影响因子：
2.5
通讯作者：
P. Benner
中科院分区：
文献类型：
--
作者：
Sridhar Chellappa;Lihong Feng;P. Benner
提出了一种简化基法离线阶段的子采样策略。该方法旨在降低与使用细采样训练集相关的可观的离线成本。该算法利用了旋转QR分解和离散经验插值方法在识别重要参数样本方面的潜力。它包括两个阶段。在第一阶段，我们在一个精细的训练集上构造解流形的低保真近似。然后，对于输出变量的可用低保真快照，我们应用pivot QR分解或离散经验插值方法在参数域中识别一组稀疏采样位置。这些点揭示了输出变量参数依赖性的结构。第二阶段使用包含比初始训练集少得多的参数的次采样训练集进行。还考虑了从经验插值方法的最新变体中得到启发的不同子采样策略。对基准示例的测试证明了新方法的合理性，并显示了它在生成可靠的降阶模型的同时，大大加快了降基方法离线阶段的潜力。
We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits the potential of the pivoted QR decomposition and the discrete empirical interpolation method to identify important parameter samples. It consists of two stages. In the first stage, we construct a low-fidelity approximation to the solution manifold over a fine training set. Then, for the available low-fidelity snapshots of the output variable, we apply the pivoted QR decomposition or the discrete empirical interpolation method to identify a set of sparse sampling locations in the parameter domain. These points reveal the structure of the parametric dependence of the output variable. The second stage proceeds with a subsampled training set containing a by far smaller number of parameters than the initial training set. Different subsampling strategies inspired from recent variants of the empirical interpolation method are also considered. Tests on benchmark examples justify the new approach and show its potential to substantially speed up the offline stage of the Reduced Basis Method, while generating reliable reduced-order models.
DOI：
10.1002/nme.2579
发表时间：
2009-09-10
影响因子：
2.9
作者：
Geuzaine, Christophe;Remacle, Jean-Francois
通讯作者：
Remacle, Jean-Francois