用条件密度估计加速贝叶斯实验设计，提升低效仿真下的决策效率。
Accelerated Bayesian Optimal Experimental Design via Conditional Density Estimation and Informative Data
- 将贝叶斯效用期望转化为独立双积分，降低计算复杂度。
- 通过高斯场比值近似与协方差筛选，高效识别关键数据集。
- 适用于仿真成本高、数据获取难的工程与科学场景。
实验设计（DOE）是提升实验结果有效性、可靠性和效率的核心方法。本文在贝叶斯框架下研究最优实验设计，利用贝叶斯定理将原为嵌套双积分的效用期望重写为独立双积分形式，显著提升数值效率。为加速效用期望计算，采用条件密度估计逼近两个高斯随机场的比值，并以协方差作为标准，筛选模型拟合与积分评估中的信息丰富数据集。在仿真效率低、原始数据获取成本高的场景下，本文系统重构了代理建模、失效概率估计与参数推断问题。理论分析与实际应用验证了该方法的有效性，展示了其在不确定性下提升实验效率与决策能力的潜力。
原文摘要 · Abstract (English)
The Design of Experiments (DOEs) is a fundamental scientific methodology that provides researchers with systematic principles and techniques to enhance the validity, reliability, and efficiency of experimental outcomes. In this study, we explore optimal experimental design within a Bayesian framework, utilizing Bayes' theorem to reformulate the utility expectation--originally expressed as a nested double integral--into an independent double integral form, significantly improving numerical efficiency. To further accelerate the computation of the proposed utility expectation, conditional density estimation is employed to approximate the ratio of two Gaussian random fields, while covariance serves as a selection criterion to identify informative datasets during model fitting and integral evaluation. In scenarios characterized by low simulation efficiency and high costs of raw data acquisition, key challenges such as surrogate modeling, failure probability estimation, and parameter inference are systematically restructured within the Bayesian experimental design framework. The effectiveness of the proposed methodology is validated through both theoretical analysis and practical applications, demonstrating its potential for enhancing experimental efficiency and decision-making under uncertainty.
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