论文标题

随机光谱嵌入

Stochastic spectral embedding

论文作者

Marelli, S., Wagner, P. -R., Lataniotis, C., Sudret, B.

论文摘要

构建可以准确模仿降低计算成本的复杂模型行为的近似值是不确定性定量的重要方面。尽管具有灵活性和效率,但经典的替代模型(例如Kriging或多项式混沌扩展)倾向于在高度非线性,本地化或非平稳的计算模型中挣扎。我们在此提出了一种基于递归嵌入局部光谱膨胀的新型顺序自适应替代模型方法。它是通过对输入结构域的脱节递归分区来实现的,该分区包括将后者依次将后者分成较小的子域,并在每个子域中构建更简单的局部光谱膨胀,从而利用了权衡复杂性与局部性。所得的扩展,我们称为“随机光谱嵌入”(SSE),是模型响应的一部分连续近似,显示出有希望的近似功能,并且具有良好的缩放,并且训练集的大小和训练集的大小均具有良好的缩放。我们最终展示了该方法如何与具有不同复杂性和输入维度的一组模型上的最新稀疏多项式混乱相比。

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models such as Kriging or polynomial chaos expansions tend to struggle with highly non-linear, localized or non-stationary computational models. We hereby propose a novel sequential adaptive surrogate modeling method based on recursively embedding locally spectral expansions. It is achieved by means of disjoint recursive partitioning of the input domain, which consists in sequentially splitting the latter into smaller subdomains, and constructing a simpler local spectral expansions in each, exploiting the trade-off complexity vs. locality. The resulting expansion, which we refer to as "stochastic spectral embedding" (SSE), is a piece-wise continuous approximation of the model response that shows promising approximation capabilities, and good scaling with both the problem dimension and the size of the training set. We finally show how the method compares favorably against state-of-the-art sparse polynomial chaos expansions on a set of models with different complexity and input dimension.

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