Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine model output uncertainties based on the uncertainty in its input variables. The most common and simplest approach to propagate the uncertainty from a model inputs to its outputs is by feeding a large number of samples to the model, known as Monte Carlo (MC) simulation which requires exhaustive sampling from the input variable distributions. However, MC simulations are impractical when models are computationally expensive. In this work, we investigate the hypothesis that while all samples are useful on average, some samples must be more useful than others. Thus, reordering MC samples and propagating more useful samples can lead to enhanced convergence in statistics of interest earlier and thus, reducing the computational burden of UP process. Here, we introduce a methodology to adaptively reorder MC samples and show how it results in reduction of computational expense of UP processes.

翻译：模型预测结果的不确定性分析是基于决策的材料设计中建立模型置信度并评估模型保真度的关键要素。不确定性传播（UP）是一种根据输入变量不确定性确定模型输出不确定性的技术。将不确定性从模型输入传播到输出的最常见且最简单的方法是向模型输入大量样本（即蒙特卡洛模拟），这需要对输入变量分布进行穷举采样。然而，当模型计算成本高昂时，蒙特卡洛模拟难以实际应用。本研究探究以下假设：尽管所有样本平均而言均有用，但某些样本必然比其他样本更有价值。因此，对蒙特卡洛样本进行重排序并优先传播更有用的样本，可提前增强感兴趣统计量的收敛性，从而降低不确定性传播过程的计算负担。本文提出了一种自适应重排序蒙特卡洛样本的方法，并展示了该方法如何降低不确定性传播过程的计算成本。