发表机构
Research Institute for Applied Mechanics, Kyushu University; Institute of Materials and Systems for Sustainability, Nagoya University; Interdisciplinary Graduate School of Engineering Sciences, Kyushu University; Computer Centre, Gakushuin University（九州大学应用力学研究所; 名古屋大学材料系统可持续发展研究所; 九州大学理工学研究科; 学习院大学计算机中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将Weisfeiler-Lehman子树核引入原子构型贝叶斯优化，显著提升了立方BC₂N基态构型搜索的效率，其评估次数远低于独热编码基线。
AI 中文摘要
原子构型的贝叶斯优化（BO）效率高度依赖于构型的编码方式。我们将Weisfeiler-Lehman（WL）子树核引入基于贝叶斯优化的构型搜索，该核将构型视为元素标记图，通过它们共享的局部结构模式数量来衡量相似性。由于该核可表示为显式特征（局部拓扑模式的L2归一化直方图）的普通内积，引入它等价于引入相应的特征：该编码作为普通描述符可接入现有BO框架。在使用通用机器学习原子间势的立方BC₂N基准基态构型搜索中，WL编码在5轮独立实验中，每轮共享100个样本的随机初始化后几乎立即达到基态，平均评估次数为108±5次，而独热编码基线需要280±122次评估；WL驱动的采样器会先耗尽简并基态组，再按能量递增顺序自底向上发现亚稳简并组。
英文摘要
The efficiency of Bayesian optimization (BO) of atomic configurations depends strongly on how configurations are encoded. We introduce the Weisfeiler-Lehman (WL) subtree kernel, which views configurations as element-labeled graphs and measures their similarity by how many local structural patterns they share, into Bayesian-optimization-based configuration search. Because this kernel is reproduced as the plain inner product of explicit features (L$^2$-normalized histograms of local topological patterns), introducing it reduces to introducing the corresponding features: the encoding enters existing BO frameworks as an ordinary descriptor. In a benchmark ground-state configuration search of cubic BC$_2$N evaluated with a universal machine-learning interatomic potential, the WL encoding reached the ground state almost immediately after a shared random initialization of 100 samples in every one of five independent rounds (108$\pm$5 evaluations on average), whereas the one-hot baseline required 280$\pm$122 evaluations; the WL-driven sampler first exhausted the degenerate ground-state group and then discovered the metastable degenerate groups from the bottom up, in order of increasing energy.
Comments6 pages, 2 figures. v2: added a control experiment without feature standardization and a bond-counting analysis of sampled configurations; conclusions unchanged
