反向传播神经网络用于预测离子液体的自扩散系数

doi:10.11949/0438-1157.20230955

摘要/Abstract

摘要：

以片段活度系数类导体屏蔽模型（COSMO-SAC）获得的电荷密度分布片段面积（S_σ ）和空穴体积（V^COSMO）为结构描述符，采用反向传播神经网络构建了可用于预测离子液体中阴阳离子自扩散系数的定量结构-性质关系（QSPR）模型——BP-ANN模型。考察了模型的适用范围与预测能力，并与线性回归得到的QSPR模型（模型I）进行了比较。发现BP-ANN模型适用的离子液体种类较广，模型在阳离子自扩散系数训练集、验证集与测试集中的决定系数R²均大于0.99，在阴离子的三个子集中的R²均大于0.98。阳离子与阴离子预测的平均绝对相对误差分别为2.8%和3.7%。线性回归的QSPR模型对应的值分别为14.54%和14.57%，即BP-ANN模型的预测效果要明显优于基于线性回归建立的模型。

关键词: 神经网络, 定量构效关系, 离子液体, 自扩散系数, 预测

Abstract:

Using the charge density distribution fragment area (S_σ ) and hole volume (V^COSMO) obtained by the fragment activity coefficient conductor-like shielding model (COSMO-SAC) as structural descriptors, we developed a quantitative structure-property relationship (QSPR) model, namely the BP-ANN model, to predict cation and anion self-diffusion coefficients of ionic liquids. The range of applicability and predictive capability of the BP-ANN model were also examined and compared with another QSPR model established by linear regression (Model I). The results revealed that the BP-ANN model can be applied to a broader range of ionic liquid species compared with Model I. The BP-ANN model achieves a high coefficient of determination (R²) value exceeding 0.99 in the training, validation, and testing dataset for cations, and surpassing 0.98 for anions across all sub-datasets. For the total dataset, the BP-ANN model yields low average absolute relative deviations (AARD) of 2.8% for cations and 3.7% for anions between calculated and experimental values, while the corresponding values for Model I are 14.54% and 14.57%, respectively. Therefore, the prediction performance of the BP-ANN model is significantly better than that of the model based on linear regression.

Key words: neural networks, QSPR, ionic liquids, self-diffusion coefficient, prediction

中图分类号:

TQ 021.4

肖拥君, 时兆翀, 万仁, 宋璠, 彭昌军, 刘洪来. 反向传播神经网络用于预测离子液体的自扩散系数[J]. 化工学报, 2024, 75(2): 429-438.

Yongjun XIAO, Zhaochong SHI, Ren WAN, Fan SONG, Changjun PENG, Honglai LIU. Prediction of self-diffusion coefficients of ionic liquids using back-propagation neural networks[J]. CIESC Journal, 2024, 75(2): 429-438.

图/表 10

图1 隐藏层最佳节点数的选取

Fig.1 Selecting an optimum number of nodes in hidden layer

表1 建模过程中实验值与计算值之间的MSE汇总

Table 1 Summary of MSE between experimental and calculated values

折数	MSE_cation×10⁴			MSE_anion×10⁴
折数	训练集	验证集	测试集	训练集	验证集	测试集
1	3.19	6.05	8.78	5.36	22.1	38.3
2	2.26	4.47	11.8	3.09	4.46	11.2
3	7.52	8.66	17.3	1.93	3.16	14.4
4	4.00	15.0	9.73	2.33	6.27	13.4
5	2.39	8.50	5.90	13.2	16.3	15.6
6	12.0	9.96	18.0	8.25	9.79	39.1
7	1.88	4.27	6.90	5.71	63.5	12.8
8	10.6	34.8	21.3	4.77	2.92	13.0
9	1.12	2.28	9.08	41.9	109	36.6
MSE	5.02	10.4	12.1	9.62	26.4	21.6

图2 离子液体自扩散系数实验值与BP-ANN模型计算值对比

Fig.2 Comparison between the experimental values of self-diffusion coefficient of ILs and the calculated values of BP-ANN model

表2 BP-ANN模型的统计参数

Table 2 Statistical parameters of BP-ANN model

项目		R² (lnD)	数据点	RMSE	AARD /%
阳离子	训练集	0.9988	864	0.23	2.5
	验证集	0.9978	108	0.45	3.3
	测试集	0.9943	111	0.54	4.4
	总集	0.9982	1083	0.30	2.8
阴离子	训练集	0.9974	728	0.30	3.4
	验证集	0.9965	91	0.39	4.2
	测试集	0.9853	92	0.88	5.0
	总集	0.9966	911	0.41	3.7

图3 离子液体自扩散系数实验值与计算值之间的相对偏差

Fig.3 Plot of relative deviation between the experimental and predicted values of self-diffusion coefficient of ILs

图4 咪唑类离子液体自扩散系数随温度变化的曲线点—实验值[34];实线—BP-ANN模型预测值

Fig.4 The self-diffusion coefficients of imidazolium ILs as a function of temperature

图5 BP-ANN模型的William图

Fig.5 William plot for BP-ANN model

图6 实验值与模型Ⅰ和BP-ANN模型计算值对比

Fig.6 Plots of experimental versus calculated resulting from Model Ⅰ and BP-ANN model

图7 离子液体自扩散系数实验值与不同模型计算值之间的相对偏差箱型图

Fig.7 Box plot representing distributions of relative deviations between experimental self-diffusion coefficients of ILs and the calculated values of two models

表3 不同种类离子液体自扩散系数实验值与计算值之间RMSE和AARD汇总

Table 3 Summary of RMSE and AARD between the experimental self-diffusion coefficients of different ILs and the calculated values of two models

IL类型		数据点	模型Ⅰ^[25]		BP-ANN 模型
IL类型		数据点	RMSE	AARD/%	RMSE	AARD/%
阳离子	咪唑类	690	2.4	15	0.33	2.3
	季铵类	184	0.61	9.5	0.20	2.9
	季类	109	0.90	20	0.22	4.0
	吡咯类	62	1.7	13	0.24	3.1
	吡啶类	8	0.93	19	0.33	4.2
	其他	30	0.45	8.3	0.39	7.3
阴离子	咪唑类	561	1.6	16	0.49	3.7
	季铵类	146	0.71	7.9	0.23	3.1
	季类	109	1.1	19	0.27	4.2
	吡咯类	60	2.5	14	0.24	3.7
	吡啶类	8	0.53	12	0.087	4.9
	其他	27	0.24	8.6	0.15	3.2

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