Learning and optimization under epistemic uncertainty with Bayesian hybrid models
Learning and optimization under epistemic uncertainty with Bayesian hybrid models
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DOI：
10.1016/j.compchemeng.2023.108430
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发表时间：
2023-09
期刊：
影响因子：
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通讯作者：
Elvis A. Eugene;Kyla D. Jones;Xian Gao;Jialu Wang;A. Dowling
中科院分区：
文献类型：
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作者：
Elvis A. Eugene;Kyla D. Jones;Xian Gao;Jialu Wang;A. Dowling
混合（即灰盒）模型是预测科学和工程的一个强大而灵活的范例。灰盒模型使用数据驱动的结构将未知或计算上难以处理的现象合并到玻璃盒机制模型中。统计学家Kennedy和O 'Hagan的开创性工作引入了一种量化认知（即模型形式）不确定性的新范式。虽然在一些工程学科中很流行，但先前使用Kennedy-O 'Hagan混合模型的工作侧重于准确估计不确定性的预测。这项工作展示了在不确定性下部署贝叶斯混合模型进行优化的计算策略。具体来说，贝叶斯混合模型的后验分布为随机规划、机会约束优化或鲁棒优化提供了原则性的不确定性集。通过两个示例研究，我们证明了混合模型的有效性，混合模型由结构不充分的玻璃盒模型和高斯过程偏差校正项组成，用于使用有限的训练数据进行决策。从这些案例研究中，我们开发了推荐的最佳实践，并探索了不同混合模型体系结构之间的权衡。
Hybrid (i.e., grey-box) models are a powerful and flexible paradigm for predictive science and engineering. Grey-box models use data-driven constructs to incorporate unknown or computationally intractable phenomena into glass-box mechanistic models. The pioneering work of statisticians Kennedy and O’Hagan introduced a new paradigm to quantify epistemic (i.e., model-form) uncertainty. While popular in several engineering disciplines, prior work using Kennedy–O’Hagan hybrid models focuses on prediction with accurate uncertainty estimates. This work demonstrates computational strategies to deploy Bayesian hybrid models for optimization under uncertainty. Specifically, the posterior distributions of Bayesian hybrid models provide a principled uncertainty set for stochastic programming, chance-constrained optimization, or robust optimization. Through two illustrative case studies, we demonstrate the efficacy of hybrid models, composed of a structurally inadequate glass-box model and Gaussian process bias correction term, for decision-making using limited training data. From these case studies, we develop recommended best practices and explore the trade-offs between different hybrid model architectures.