We propose an efficient surrogate modeling technique for uncertainty quantification. The method is based on a well-known dimension-adaptive collocation scheme. We improve the scheme by enhancing sparse polynomial surrogates with conformal maps and adjoint error correction. The methodology is applied to Maxwell's source problem with random input data. This setting comprises many applications of current interest from computational nanoplasmonics, such as grating couplers or optical waveguides. Using a non-trivial benchmark model we show the benefits and drawbacks of using enhanced surrogate models through various numerical studies. The proposed strategy allows us to conduct a thorough uncertainty analysis, taking into account a moderately large number of random parameters.

中文翻译：

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增强的自适应替代模型在纳米等离子体不确定性量化中的应用

我们提出了一种用于不确定性量化的有效替代建模技术。该方法基于众所周知的维度自适应搭配方案。我们通过使用保角映射和伴随纠错来增强稀疏多项式代理来改进该方案。该方法应用于具有随机输入数据的麦克斯韦源问题。这种设置包括当前来自计算纳米等离子体的许多应用，例如光栅耦合器或光波导。使用非平凡的基准模型，我们通过各种数值研究展示了使用增强代理模型的优点和缺点。所提出的策略允许我们进行彻底的不确定性分析，同时考虑到中等数量的随机参数。