Nested Bayesian Optimization for Computer Experiments
Nested Bayesian Optimization for Computer Experiments
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DOI：
10.1109/tmech.2022.3202079
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
Yan Wang;M. Wang;Areej AlBahar;Xiaowei Yue
中科院分区：
文献类型：
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作者：
Yan Wang;M. Wang;Areej AlBahar;Xiaowei Yue
计算机实验可以模拟物理系统，帮助计算研究，并产生解析解。它们已被广泛用于许多工程应用（例如，航空航天、汽车、能源系统）。传统的贝叶斯优化没有将嵌套结构纳入计算机实验中。本文提出了一种新的嵌套贝叶斯优化方法，用于具有多步或层次特征的复杂计算机实验。我们证明了嵌套输出的理论性质，给定的嵌套输出的分布是高斯或非高斯。导出了嵌套期望改进的封闭形式。我们还提出了嵌套贝叶斯优化的计算算法。三个数值研究表明，所提出的嵌套贝叶斯优化方法优于五个基准贝叶斯优化方法，忽略了内部计算机代码的中间输出。算例表明，该方法能有效地减小复合材料结构装配过程中的残余应力，避免收敛于局部最优。
Computer experiments can emulate the physical systems, help computational investigations, and yield analytic solutions. They have been widely employed with many engineering applications (e.g., aerospace, automotive, energy systems). Conventional Bayesian optimization did not incorporate the nested structures in computer experiments. This article proposes a novel nested Bayesian optimization method for complex computer experiments with multistep or hierarchical characteristics. We prove the theoretical properties of nested outputs given that the distribution of nested outputs is Gaussian or non-Gaussian. The closed forms of nested expected improvement are derived. We also propose the computational algorithms for nested Bayesian optimization. Three numerical studies show that the proposed nested Bayesian optimization method outperforms the five benchmark Bayesian optimization methods that ignore the intermediate outputs of the inner computer code. The case study shows that the nested Bayesian optimization can efficiently minimize the residual stress during composite structures assembly and avoid convergence to local optima.