In many engineering applications, a single high-fidelity model produces multiple quantities of interest (QoIs) under the same input parameters, e.g. finite element models of complex physical systems. To alleviate the high computational cost of direct model evaluations, surrogate models are widely used to construct efficient approximations of model responses. Naturally, the accuracy of surrogates strongly depends on the quality of the experimental design (ED). However, a single ED may not provide an adequate representation for all outputs simultaneously, especially when different outputs exhibit varying sensitivities to the input variables. A straightforward solution is to perform separate sampling for each output, but this results in increased sampling complexity and computational cost. From a statistical perspective, such an approach also ignores potential correlations among all outputs and may compromise data consistency. To address this issue, an adaptive sequential sampling method for constructing polynomial chaos expansion surrogate models is generalized for vector valued QoIs. The method sequentially selects new samples from a candidate pool based on their local contribution to the output variance, while balancing distance-based exploration of the input space and exploitation of aggregated variance information across all outputs. Its performance is compared with non-sequential Latin Hypercube Sampling through several numerical examples from engineering problems. Numerical results demonstrate that the proposed strategy improves both surrogate accuracy and stability, and provides a more reliable estimation of second-order statistics.

翻译：在许多工程应用中，单个高保真模型在相同输入参数下会产生多个感兴趣量（QoIs），例如复杂物理系统的有限元模型。为缓解直接模型评估的高计算成本，代理模型被广泛用于构建模型响应的高效近似。自然地，代理模型的准确性强烈依赖于实验设计（ED）的质量。然而，单个实验设计可能无法同时为所有输出提供充分表示，尤其是当不同输出对输入变量表现出不同敏感性时。一个直接的解决方案是为每个输出分别进行采样，但这会导致采样复杂性和计算成本增加。从统计角度来看，这种方法也忽略了所有输出间的潜在相关性，可能损害数据一致性。为解决此问题，提出了一种自适应序贯采样方法，用于构建面向向量值QoIs的多项式混沌展开代理模型。该方法通过评估候选样本对输出方差的局部贡献，在平衡输入空间的基于距离的探索与所有输出聚合方差信息的利用的基础上，从候选池中序贯选取新样本。其性能通过工程问题的多个数值算例与非序贯拉丁超立方采样进行了比较。数值结果表明，所提策略同时提升了代理模型的准确性与稳定性，并提供了对二阶统计量的更可靠估计。