利用已知内部结构的灰盒多模型集合的贝叶斯仿真
Bayesian Emulation of Grey-Box Multi-Model Ensembles Exploiting Known Interior Structure
AI总结：
本研究提出一种灰盒多模型集合的贝叶斯仿真方法框架，通过子采样、分而治之和结构化仿真等技术提升物理可解释性与预测准确性，并应用于TNO OLYMPUS井控制优化挑战赛。
摘要：
计算机模型被广泛用于研究复杂的现实世界物理系统。然而，它们的直接使用存在主要局限性，包括：复杂的结构；大量的输入和输出；以及漫长的评估时间。贝叶斯仿真器是应对这些挑战的有效手段，为计算机模型输出提供快速高效的统计近似。通常假设计算机模型表现得像一个“黑盒”函数，在评估之前对其输出一无所知。这确保了仿真器的通用性，但与利用这种受约束或结构化输出行为的知识相比，可能会限制其准确性。我们假设一个“灰盒”计算机模型，并开发了一个用于其分析的方法论工具包。这包括：多模型集合子采样，以识别具有代表性的模型子集，从而降低计算开销；构建用于优化或决策支持的目标贝叶斯设计；一种用于仿真输出总和的“分而治之”方法；通过分割参数空间和施加截断，利用组成输出的已知受约束和结构化行为的结构化仿真器；时间序列输出总和的仿真；以及多模型集合输出的仿真。结合这些方法建立了一个分层仿真框架，该框架实现了更高的物理可解释性和更准确的仿真器预测。本研究受石油工业中具有重要商业价值的TNO OLYMPUS井控制优化挑战赛的启发并应用于该挑战赛，我们将其重新表述为不确定性下的决策支持问题。因此，我们鼓励用户检查他们的“黑盒”模拟器，以实现卓越的仿真器准确性。
英文摘要：
Computer models are widely used to study complex real world physical systems. However, there are major limitations to their direct use including: their complex structure; large numbers of inputs and outputs; and long evaluation times. Bayesian emulators are an effective means of addressing these challenges providing fast and efficient statistical approximation for computer model outputs. It is commonly assumed that computer models behave like a ``black-box'' function with no knowledge of the output prior to its evaluation. This ensures that emulators are generalisable but potentially limits their accuracy compared with exploiting such knowledge of constrained or structured output behaviour. We assume a ``grey-box'' computer model and develop a methodological toolkit for its analysis. This includes: multi-model ensemble subsampling to identifying a representative model subset to reduce computational expense; constructing a targeted Bayesian design for optimisation or decision support; a ``divide-and-conquer'' approach to emulating sums of outputs; structured emulators exploiting known constrained and structured behaviour of constituent outputs through splitting the parameter space and imposing truncations; emulation of sums of time series outputs; and emulation of multi-model ensemble outputs. Combining these methods establishes a hierarchical emulation framework which achieves greater physical interpretability and more accurate emulator predictions. This research is motivated by and applied to the commercially important TNO OLYMPUS Well Control Optimisation Challenge from the petroleum industry which we re-express as a decision support under uncertainty problem. We thus encourage users to examine their ``black-box'' simulators to achieve superior emulator accuracy.
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