基于晶体图卷积神经网络的晶格能回归模型

doi:10.11949/0438-1157.20240849

摘要/Abstract

摘要：

晶格能是决定晶体热力学稳定性的关键物理性质，对药物多晶型稳定性的筛选具有指导意义。晶格能的获取方式通常为实验试错和基于分子/量子力学的理论计算，对于数量庞大的晶型结构，两种方法均费时费力。提出一种基于密度泛函理论（density functional theory，DFT）和晶体图卷积神经网络（crystal graph convolutional neural networks，CGCNN）的晶格能回归模型。首先采用自洽屏蔽多体色散校正的DFT方法计算晶格能，建立包含酸、醇、酰胺、氨基酸、酸酐等248种晶型的晶格能数据集；基于所建立的数据集，采用CGCNN进一步建立晶型和晶格能之间的定量回归模型，该模型训练集和测试集的MAPE分别为1.24%和5.04%，R²分别为0.9978和0.9750，表明该模型具有较好的预测效果，可以为高通量筛选稳定的晶型提供理论指导。

关键词: 晶格能, 多晶型, 密度泛函理论, 神经网络, 回归模型

Abstract:

The lattice energy is a critical physical property determining the thermodynamic stability of crystals and holds instructive significance in screening the stability of polymorphism. Lattice energy is usually obtained by experimental trial and error as well as theoretical calculation based on molecular/quantum mechanics. For a large number of crystal structures, both methods are time-consuming and laborious. In this paper, a lattice energy regression model based on density functional theory (DFT) and crystal graph convolutional neural networks (CGCNN) is proposed. First, the lattice energies were calculated using the range-separated self-consistent screened many-body dispersion corrected DFT method. A dataset comprising lattice energies for 248 crystal structures including acids, alcohols, amides, amino acids, and anhydrides was established. Subsequently, leveraging this dataset, a crystal graph convolutional neural networks model was employed to establish a quantitative regression model for the relationship between crystal structures and lattice energies, which demonstrated promising predictive performance with mean absolute percentage error (MAPE) values of 1.24% for the training set and 5.04% for the test set, and R² values of 0.9978 and 0.9750, respectively. The results show that the model has a good predictive performance which can provide theoretical guidance and technical support for high-throughput screening of stable crystal forms.

Key words: lattice energy, polymorphism, density function theory, neural networks, regression model

中图分类号:

TP 183

郑欣雨, 任泽华, 周利, 柴士阳, 吉旭. 基于晶体图卷积神经网络的晶格能回归模型[J]. 化工学报, 2025, 76(3): 1084-1092.

Xinyu ZHENG, Zehua REN, Li ZHOU, Shiyang CHAI, Xu JI. Lattice energy regression model based on crystal graph convolutional neural networks[J]. CIESC Journal, 2025, 76(3): 1084-1092.

图/表 7

图1 基于晶体图卷积神经网络的晶格能回归模型基本框架

Fig.1 Basic framework of lattice energy regression model based on crystal graph convolutional neural network

图2 数据分布图：涵盖酸、醇、酰胺、氨基酸、酸酐等不同官能团的化合物以及同一分子不同晶体结构

Fig.2 The distribution of data points: compounds with different functional groups, such as acids, alcohols, amides, amino acids and anhydrides, as well as different crystal structures of the same molecule

图3 CGCNN神经网络结构图

Fig.3 Structure diagram of CGCNN neural network

表1 模型训练参数设置

Table 1 Model training parameter setting

参数	设定值
批量大小	8
周期	800
学习率	0.01（动态）
损失函数	MSELoss
优化程序	SGD
卷积层数	3
卷积层神经元数	128
激活函数	SoftPlus

图4 不同超参数下训练集、验证集和测试集的性能：(a)卷积层数为1~15时模型的性能变化曲线；(b)神经元数为64~256时模型的性能变化曲线

Fig.4 Performance of training set, validation set and test set under different hyperparameters: (a) performance curve of the model when the number of convolution layers is 1—15; (b) performance curve of the model when the number of neurons is 64—256

图5 32种晶体结构实验晶格能和计算晶格能的比较

Fig.5 Comparison of experimental lattice energy with calculated lattice energy of 32 crystal structures

图6 模型训练结果：(a)损失衰减曲线，在第333个epoch得到最小损失；(b)训练集结果；(c)验证集结果；(d)测试集结果，阴影部分表示晶格能计算值和预测值差异小于等于10 kJ·mol-1的范围

Fig.6 Model training results: (a) loss decline curve, the minimum loss is achieved at the 333rd epoch; (b) training set results; (c) validation set results; (d) test set results, the shaded area indicates the range where the difference between the calculated and predicted values of the lattice energy is less than or equal to 10 kJ·mol-1

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