SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page A1582-A1608, January 2020.
The discrete empirical interpolation method (DEIM) is a popular technique for nonlinear model reduction, and it has two main ingredients: an interpolating basis that is computed from a collection of snapshots of the solution, and a set of indices which determine the nonlinear components to be simulated. The computation of these two ingredients dominates the overall cost of the DEIM algorithm. To specifically address these two issues, we present randomized versions of the DEIM algorithm. There are three main contributions of this paper. First, we use randomized range finding algorithms to efficiently find an approximate DEIM basis. Second, we develop randomized subset selection tools, based on leverage scores, to efficiently select the nonlinear components. Third, we develop several theoretical results that quantify the accuracy of the randomization on the DEIM approximation. We also present numerical experiments that demonstrate the benefits of the proposed algorithms.

中文翻译：

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非线性模型约简的随机离散经验插值方法

SIAM科学计算杂志，第42卷，第3期，第A1582-A1608页，2020年1月。
离散经验插值方法（DEIM）是非线性模型简化的一种流行技术，它具有两个主要成分：从解决方案快照的集合中计算出的插值基础，以及用于确定非线性分量的一组指标。被模拟。这两个因素的计算决定了DEIM算法的总成本。为了专门解决这两个问题，我们提出了DEIM算法的随机版本。本文主要有三点贡献。首先，我们使用随机测距算法来有效地找到近似DEIM基础。其次，我们基于杠杆得分开发随机子集选择工具，以有效选择非线性成分。第三，我们开发了一些理论结果，这些结果量化了DEIM近似上的随机化精度。我们还提供了数值实验，证明了所提出算法的优势。