在碳捕集与封存应用中诱导排列不变的先验分布
Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications
AI总结：
本文提出了一种新的高斯过程核（GP-Perm），用于在碳捕集与封存项目中处理排列对称性问题，同时结合深度核学习模型（DKL-DS）以学习排列不变的嵌入，通过八个用例评估了所提出的方法。
摘要：
贝叶斯优化是一种迭代方法，专门用于优化昂贵的黑盒目标函数。像高斯过程（GP）这样的代理模型是贝叶斯优化的黄金标准，但当输入具有排列对称性时，常用的内核在处理无序项集时效率低下。受此问题的启发，我们转向在碳捕集与封存项目中使用排列不变的贝叶斯优化进行井位布置。高保真黑盒模拟器被指示在群控制下操作井，导致注入器和生产器群中出现无法被标准GP内核利用的排列对称性。在本工作中，我们的主要贡献是一种新的高斯过程内核（GP-Perm），通过比较集合的诱导经验表示之间的稳定分歧来编码排列不变性，并可以与标准内核结合以处理额外的向量值输入。作为学习不变的基线，我们还考虑了使用深度集架构的深度核学习模型（DKL-DS）来学习排列不变的嵌入。我们评估了所提出的方法在8个用例中的表现，包括七个合成基准和一个现实的CCS案例研究（Johansen构造）
英文摘要：
Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with permutation symmetries, as the most common kernels employed are better suited for vector inputs rather than unordered sets of items. Motivated by this issue, we turn to permutation invariant Bayesian Optimization for well placement in Carbon Capture and Storage projects. The high fidelity black box simulator is instructed to operate wells under group control, giving rise to permutation symmetries within injector and producer groups that cannot be exploited with standard GP kernels. In this work, our main contribution is a novel Gaussian Process kernel (GP-Perm) that encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations, and can be combined with standard kernels for additional vector-valued inputs. As a learned invariant baseline, we also consider a Deep Kernel Learning model (DKL-DS) using the Deep Sets architecture to learn a permutation-invariant embedding. We evaluate the proposed methodology across 8 use cases, comprising seven synthetic benchmarks and one realistic CCS case study (Johansen formation)
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
