AI 中文总结
针对有限设计集上昂贵计算模型，提出自适应贝叶斯最优实验设计算法，集成加速嵌套蒙特卡罗估计器等技术，通过自举抽样估计概率迭代消除劣质设计，降低计算成本并实现高可靠性，适用于大规模工程应用。
AI 中文摘要
贝叶斯校准是识别复杂大规模计算模型中参数的强大框架。但校准过程中数据不足或不合适时，参数存在显著不确定性，影响决策和系统理解。在许多应用中，生成数据的实验受设计变量影响，且常只能从有限设计集中选择。本文针对有限设计集提出一种自适应贝叶斯最优实验设计算法，专为昂贵计算模型应用定制。该方法集成加速嵌套蒙特卡罗估计器以重用参数样本减少模型评估，采用公共随机数和Rao--Blackwellization减少成对预期信息增益比较中的方差。通过自举抽样估计一种设计优于另一种的概率以支持算法决策，从小样本量开始迭代消除劣质设计，仅将额外计算资源分配给有前景的候选设计，直到只剩一个设计。该方法以大幅降低的计算成本实现高可靠性，适用于大规模工程应用。
英文摘要
Bayesian calibration is a powerful framework for identifying parameters in complex and large-scale computational models. However, when there is insufficient or poorly suited data for the calibration process, significant uncertainty about the identified parameters remains. This uncertainty can hinder effective decision-making and understanding of the system. In many applications, the experiment that generates the data can be influenced by design variables, such as sensor placements, loading conditions, or test configurations. Often, however, these design variables can not be chosen arbitrarily but only from a finite set of possible experimental designs. We propose an adaptive algorithm for Bayesian optimal experimental design over a finite design set, specifically tailored for applications involving expensive computational models. The method integrates an accelerated nested Monte Carlo estimator that reuses parameter samples to reduce model evaluations. Additionally, it employs common random numbers and Rao--Blackwellization to reduce variance in pairwise expected information gain comparisons. To support decision-making within the algorithm, we estimate the probability that one design outperforms another using bootstrap sampling. Starting with small sample sizes, the algorithm iteratively eliminates inferior designs based on these probabilistic comparisons, allocating additional computational effort only to promising candidates until a single design remains. The resulting approach achieves high reliability at substantially reduced computational cost, making it well-suited for large-scale engineering applications.
Comments24 pages, 13 figures
