Bayesian optimization of functional output in inverse problems
Bayesian optimization of functional output in inverse problems
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DOI：
10.1007/s11081-021-09677-1
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发表时间：
2021-09
影响因子：
2.1
通讯作者：
Chaofan Huang;Yi Ren;Emily K. McGuinness;M. Losego;Ryan P. Lively;V. R. Joseph
中科院分区：
文献类型：
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作者：
Chaofan Huang;Yi Ren;Emily K. McGuinness;M. Losego;Ryan P. Lively;V. R. Joseph
基于气相渗透过程中反应-扩散输运模型的参数辨识问题，我们提出了一种贝叶斯优化方法来求解反问题，该反问题旨在找到一个能够实现期望功能输出的输入设置。与标准的单目标贝叶斯优化算法相比，该算法有以下改进：(1)利用广义卡方分布作为反问题中距离平方目标函数的更合适的预测分布；(2)应用泛函主成分分析降低函数响应数据的维数。它允许预测分布的有效逼近和期望改进获取函数的后续计算。
Motivated by the parameter identification problem of a reaction-diffusion transport model in a vapor phase infiltration processes, we propose a Bayesian optimization procedure for solving the inverse problem that aims to find an input setting that achieves a desired functional output. The proposed algorithm improves over the standard single-objective Bayesian optimization by (i) utilizing the generalized chi-square distribution as a more appropriate predictive distribution for the squared distance objective function in the inverse problems, and (ii) applying functional principal component analysis to reduce the dimensionality of the functional response data, which allows for efficient approximation of the predictive distribution and the subsequent computation of the expected improvement acquisition function.