Polynomial chaos expansion (PCE) has been widely used to facilitate uncertainty quantification and stochastic computations for complex systems. Multi-fidelity approaches expedite the construction of the PCE surrogate by blending the efficiency of low-fidelity models and accuracy of high-fidelity models. In this work, we propose a novel non-intrusive multi-fidelity sampling approach that exploits the low computational cost of the low-fidelity model to select a set of high-yield sampling locations for the high-fidelity model. Particularly, the proposed approach draws upon the unique features of the Kaczmarz updating scheme to design a greedy search that explores a large pool of low-fidelity samples and iteratively removes the least contributive ones. Facilitated via a subset updating strategy, the search lands on a small subset of the initial pool which is then used to construct the PCE surrogate for the high-fidelity model. The proposed approach offers a remarkable computational performance, practically delivering accurate results with a high-fidelity sample size about the cardinality of the basis, and as such is amenable to efficient uncertainty quantification on fixed and limited budget. We provide several numerical examples that demonstrate the promise of the proposed approach in substantially reducing the number of high-fidelity samples required for accurate construction of the PCE surrogate.

多项式混沌展开 (PCE) 已被广泛用于促进复杂系统的不确定性量化和随机计算。多保真方法通过混合低保真模型的效率和高保真模型的准确性来加快 PCE 代理的构建。在这项工作中，我们提出了一种新颖的非侵入式多保真采样方法，该方法利用低保真模型的低计算成本为高保真模型选择一组高收益采样位置。特别是，所提出的方法利用 Kaczmarz 更新方案的独特特征来设计贪婪搜索，该搜索探索大量低保真样本并迭代删除贡献最小的样本。通过子集更新策略促进，搜索落在初始池的一个小子集上，然后用于构建高保真模型的 PCE 代理。所提出的方法提供了卓越的计算性能，实际上以关于基数的高保真样本大小提供了准确的结果，因此适用于固定和有限预算的有效不确定性量化。我们提供了几个数值例子，证明了所提出的方法在大幅减少准确构建 PCE 代理所需的高保真样本数量方面的前景。实际上，通过关于基数的高保真样本量提供准确的结果，因此可以在固定和有限预算下进行有效的不确定性量化。我们提供了几个数值例子，证明了所提出的方法在大幅减少准确构建 PCE 代理所需的高保真样本数量方面的前景。实际上，通过关于基数的高保真样本量提供准确的结果，因此可以在固定和有限预算下进行有效的不确定性量化。我们提供了几个数值例子，证明了所提出的方法在大幅减少准确构建 PCE 代理所需的高保真样本数量方面的前景。