论文标题
S-OPT：用于减少顺序模型中过度还原的点选择算法
S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models
论文作者
论文摘要
虽然基于投影的减少订单模型可以减少全订单解决方案的维度，但所得减少的模型仍可能包含随着完整订单维度扩展的术语。高还原技术是基于抽样的方法，可以通过近似较小的维度近似此类术语来进一步降低这种计算复杂性。这项工作的目的是引入Shin和Xiu开发的点选择算法[Siam J. Sci。 Comput。，38（2016），pp。A385-A411]，作为一种超还原方法。选择算法最初是作为不确定性定量的随机搭配方法提出的。由于该算法的目的是最大化测量柱正交性和决定因素的数量S，因此我们将算法称为S-OPT。提供了数值示例，以证明S-OPT的性能并将其性能与过度采样的离散经验插值（DEIM）算法进行比较。我们发现，使用S-OPT算法显示以更高的精度预测给定数量的索引的完整解决方案。
While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce a points selection algorithm developed by Shin and Xiu [SIAM J. Sci. Comput., 38 (2016), pp. A385--A411], as a hyper-reduction method. The selection algorithm is originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity S that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with an over-sampled Discrete Empirical Interpolation (DEIM) algorithm. We found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy for a given number of indices.
