为碳捕集项目优化井位布局，提出可处理无序组的新型高斯过程核
Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications
- 设计新核函数GP-Perm，通过集合经验表示的稳定散度实现排列不变性
- 在8个场景中验证，相较标准核提升优化效率，真实案例（Johansen地层）表现显著
- 适合处理具有对称性的复杂工程优化，如井群布局、分子设计等
贝叶斯优化是一种迭代方法，适用于优化昂贵的黑箱目标函数。主流代理模型如高斯过程（GP）在输入具有排列对称性时效率低下，因常用核函数更适合向量输入而非无序项集合。针对此问题，本文研究了碳捕集与封存（CCS）项目中的井位优化，其中注采井组在群体控制下产生排列对称性，标准GP核无法利用。本文提出一种新型高斯过程核（GP-Perm），通过比较集合诱导的经验表示之间的稳定散度来编码排列不变性，并可与标准核结合处理额外的向量输入。作为学习型基线，还采用基于Deep Sets架构的深度核学习模型（DKL-DS）学习排列不变嵌入。在7个合成基准和1个真实案例（Johansen地层）共8个用例中评估该方法，结果表明其显著优于传统方法。
原文摘要 · Abstract (English)
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)
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