机器学习探索含原子空位石墨烯的缺陷拓扑与热力学稳定性
Machine-Learning Exploration of Defect Topologies and Thermodynamic Stability in Graphene with Atomic Vacancies
AI总结：
本研究结合半经验热力学、可解释机器学习和符号回归，映射了含原子空位石墨烯的稳定性景观，识别出关键变量并导出高精度解析表达式，为二维材料缺陷工程提供可迁移方法。
AI中文摘要：
原子空位及空位聚集体控制着石墨烯的热力学稳定性和功能响应，然而，由许多空位在可变浓度和间距下所张成的构型空间过于庞大，无法通过第一性原理方法进行穷举映射。在此，我们通过结合半经验原子热力学、可解释机器学习和符号回归，来映射并合理化这一稳定性景观。通过改变空位浓度和空位间距（直至第四近邻），从72原子晶胞构建了数百个缺陷超胞，并使用MOPAC中的PM7哈密顿量进行弛豫，以生成热作为稳定性度量。每个结构都用动态碰撞指纹（Dynamic Collision Fingerprint）编码，这是一种平移和旋转不变描述符，将局部拓扑映射为虚拟探针粒子的输运类统计量。通过贝叶斯超参数搜索优化的梯度提升决策树模型，在独立测试集上再现生成热，均方根误差约为23.5 kcal/mol，且无过拟合迹象；SHAP分析确定缺陷浓度和空位间距是主导稳定性的两个变量。随后，符号回归将学习到的映射压缩为紧凑的闭式表达式，其再现生成热的决定系数R²=0.9966，平均绝对误差为15.51 kcal/mol，均方根误差为24.18 kcal/mol。该工作流程将高维结构-稳定性问题转化为可解释的解析定律，为二维材料中的理性缺陷工程提供了可迁移的途径。
英文摘要：
Atomic vacancies and vacancy aggregates control the thermodynamic stability and the functional response of graphene, yet the configurational space spanned by many vacancies at variable concentration and separation is too large to be mapped exhaustively by first-principles methods. Here, we map and rationalize this stability landscape by combining semiempirical atomistic thermodynamics, interpretable machine learning, and symbolic regression. Several hundred defective supercells, built from a 72-atom cell by varying the vacancy concentration and the inter-vacancy distance up to the fourth neighbor, were relaxed with the PM7 Hamiltonian in MOPAC, and the heat of formation was adopted as the stability metric. Each structure was encoded with the Dynamic Collision Fingerprint, a translationally and rotationally invariant descriptor that maps the local topology onto transport-like statistics of virtual probe particles. A gradient boosted decision tree model, optimized by Bayesian hyperparameter search, reproduces the heat of formation of an independent test set with a root mean squared error of approximately 23.5~kcal/mol and no evidence of overfitting, and a SHAP analysis identifies the defect concentration and the inter-vacancy distance as the two variables that dominate the stability. Symbolic regression then condenses the learned mapping into a compact closed-form expression that reproduces the heat of formation with a coefficient of determination of $R^{2} = 0.9966$, a mean absolute error of 15.51~kcal/mol, and a root mean squared error of 24.18~kcal/mol. The workflow turns a high-dimensional structure--stability problem into an interpretable analytical law, providing a transferable route to rational defect engineering in two-dimensional materials.
