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法

离散经验插值法 (DEIM) 是一种流行的非线性模型简化技术，它有两个主要成分：从解的快照集合计算的插值基和确定要模拟的非线性分量的一组索引。这两个成分的计算在 DEIM 算法的总成本中占主导地位。为了专门解决这两个问题，我们提出了 DEIM 算法的随机版本。本文的主要贡献有三点。首先，我们使用随机测距算法来有效地找到近似的 DEIM 基础。其次，我们开发了基于杠杆分数的随机子集选择工具，以有效地选择非线性组件。第三，我们开发了几个理论结果，这些结果量化了 DEIM 近似随机化的准确性。我们还提供了数值实验，证明了所提出算法的好处。