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Surrogate modeling based on resampled polynomial chaos expansions

机译：基于重采采样多项式混沌扩建的代理建模

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摘要

In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite-element and finite-difference time-domain methods. Recently, efforts have been made on improving the prediction performance of the PCE-based model and building efficiency by only selecting the influential basis polynomials (e.g., via the approach of least angle regression). This paper proposes an approach, named as resampled PCE (rPCE), to further optimize the selection by making use of the knowledge that the true model is fixed despite the statistical uncertainty inherent to sampling in the training. By simulating data variation via resampling (k-fold division utilized here) and collecting the selected polynomials with respect to all resamples, polynomials are ranked mainly according to the selection frequency. The resampling scheme (the value of k here) matters much and various configurations are considered and compared. The proposed resampled PCE is implemented with two popular selection techniques, namely least angle regression and orthogonal matching pursuit, and a combination thereof. The performance of the proposed algorithm is demonstrated on two analytical examples, a benchmark problem in structural mechanics, as well as a realistic case study in computational dosimetry.
机译：在代理建模中，多项式混沌扩展（PCE）宽容地利用来表示随机模型响应，该响应是计算昂贵的并且通常通过确定性数值建模方法获得，包括有限元和有限差时域方法。最近，通过仅选择有影响力的基础多项式（例如，通过最小角度回归的方法）来改善基于PCE的模型和建筑效率的预测性能。本文提出了一种命名为重采样PCE（RPCE）的方法，以利用真实模型在训练中采样所固有的统计不确定性来进一步优化选择。通过模拟通过重采样（这里使用的k折划分）和收集所选择的多项式的数据变化并相对于所有重生，多项式主要根据选择频率排序。重采样方案（此处的值）很重要，并进行比较各种配置。所提出的重采采样的PCE用两个普遍的选择技术，即最小角度回归和正交匹配追踪来实现，以及其组合。在两个分析示例中，在结构力学中的基准问题以及计算剂量测定中的基准问题，证明了所提出的算法的性能。

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