论文标题
$ hp $ - 适应性多元素随机搭配方法，用于替代建模，并重复使用信息
An $hp$-adaptive multi-element stochastic collocation method for surrogate modeling with information re-use
论文作者
论文摘要
本文介绍了$ HP $ - 适应性的多元元素随机搭配方法，该方法还允许在$ h $ - 或$ p $ - 重新填充期间重新使用现有的模型评估。搭配方法基于加权Leja节点。 $ h $ - 再填充后，通过在每个新创建的子元素上以层次结构方式添加和分类Leja节点来稳定本地插值。对于$ p $ - 再填充，本地多项式近似基于总学位或维度自适应基础。该方法应用于向前和逆不确定性量化的背景，以处理非平滑或强烈局部响应表面。与竞争方法相比，在几种测试案例中评估了所提出的方法的性能。
This paper introduces an $hp$-adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either $h$- or $p$-refinement. The collocation method is based on weighted Leja nodes. After $h$-refinement, local interpolations are stabilized by adding and sorting Leja nodes on each newly created sub-element in a hierarchical manner. For $p$-refinement, the local polynomial approximations are based on total-degree or dimension-adaptive bases. The method is applied in the context of forward and inverse uncertainty quantification to handle non-smooth or strongly localised response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods.
