Npj Comput. Mater.: 离子介电极化率数据缺失？机器学习填补其遗憾瑕疵！
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介电常数决定电介质材料的实际应用，准确计算和预测介电常数是实现微波介质材料按需设计的重要一环。准确计算和预测介电常数是实现微波介质材料按需设计的重要一环。经典介电常数计算公式Clausius-Mossotti方程和最新报道的介电常数预测模型均指出分子介电极化率是预测介电常数的决定性参量，而该参量可通过加和离子介电极化率（αD）得到。然而，当今最具影响力的、由Shannon于1993年给出的αD数据库在5G/6G时代面临着三大挑战：①数据量少、②离子基本属性对αD的影响考虑较少、③仅面向低频段（kHz ~ MHz），因此不能满足面向GHz频段应用的新型微波介质材料的介电常数准确计算和预测。机器学习方法在材料性能预测和挖掘数据背后隐含物理关系等问题中表现出定量、准确、高效、低成本等优势，这为αD数据库的优化及拓展开辟了新路径。
中国科学院上海硅酸盐研究所的刘志甫研究员团队采用多元线性回归和支持向量机方法，优化并拓展了离子介电极化率数据库，实现αD数据准确性的提升，同时将数据量从61种大幅扩充至915种，覆盖92种元素。该工作基于文献报道的334种微波介质陶瓷的介电常数数据，依据目前αD数据的误差程度，采用四阶段多元线性回归方法对不同αD数据进行优化。基于优化后的数据库，采用多种机器学习模型尝试建立αD值与离子基本属性之间的定量关系，并利用最优模型拓展αD数据库。模型寻优表明，最优模型基于支持向量机算法，包含原子序数（N）、价态（V）、配位数（CN）和离子半径（IR）四个特征量。该工作还结合电介质理论知识和归因分析SHAP方法，讨论了离子基本属性对αD值的作用机制，并发现前人的研究忽视了V和CN对αD值的重要影响，所总结的αD值与离子半径三次方之间的正线性关系并非总是成立：对于V和CN相同的离子，IR的变化由N引起，规律成立；但对于V和N相同的离子，IR的变化由CN引起，规律失效。基于该工作，作者还建立了一个在线αD数据库（https://qincas.gitee.io/idp-ml/），为微波介质材料领域的研究者提供参考。
Fig. 1 The performances of the optimal ML model
Fig. 2 The variations of the ML extended αD values of ions with different valence states and coordination numbers as a function of the cube of the ionic radius
Optimizing and extending ion dielectric polarizability database for microwave frequencies using machine learning methods
Jincheng Qin, Zhifu Liu, Mingsheng Ma & Yongxiang Li
Permittivity at microwave frequencies determines the practical applications of microwave dielectric ceramics. The accuracy and universality of the permittivity prediction by Clausius-Mossotti equation depends on the dielectric polarizability (αD) database. The most influential αD database put forward by Shannon is facing three challenges in the 5G era: (1) Few data, (2) Simplistic relation and (3) Low frequency (kHz ~ MHz) oriented. Here, we optimized and extended the Shannon’s database for microwave frequencies by the four-stage multiple linear regression and support vector machine model. In comparison with the conventional database, the optimized and extended databases achieved higher accuracy and expanded the amount of data from 60 to more than 900. Besides, we analyzed the relationships between αD and ion characteristics, including ionic radius (IR), atomic number (N), valence state (V) and coordination number (CN). We found that the positive cubic law of “αD ~ IR3” discussed in Shannon’s work was valid for the IR changed by the N, but invalid for the change caused by the CN.
Fig. 3 The tendency of the ML extended αD values with the increase of the ionic radius of ions with the same atomic number and valence state, but different coordination number
Fig. 4 The comparison of the data amounts and accuracies of the αD databases
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