迁移学习预测金属/共价有机骨架材料内小分子气体自扩散系数研究

doi:10.6023/A25110385

摘要/Abstract

气体分子在金属(Metal-organic Frameworks, MOFs)/共价(Covalent-organic Frameworks, COFs)有机骨架材料内的扩散系数是重要的物化性质, 显著影响其在气体存储与分离、化学催化等应用中的性能. 分子动力学模拟是分析扩散系数的主要手段之一. 随着新型纳米多孔材料种类的高速增长, 机器学习辅助分子动力学模拟预测扩散系数策略备受关注. 但机器学习也面临着不同数据库及各类气体分子存在差异导致泛化预测精度受限的问题, 尤其是各类材料数据库发展显著失衡, 迁移学习能有效解决此问题, 提升泛化预测性能. 本研究通过分子动力学模拟预测8种气体分子(H₂、CH₄、H₂S、CO₂、N₂、C₂H₆、C₃H₈、C₄H₁₀)在MOFs骨架内的自扩散系数, 通过集成和神经网络两类算法进行迁移学习预测COFs内扩散系数, 发现轻量梯度提升树模型迁移后预测精度最高, 且气体的动力学直径、极化率和结构的受限孔直径是重要的描述符. 本工作证明了迁移学习在多类数据库中辅助预测扩散系数的可行性, 为新型纳米多孔材料的泛化学习提供了新的策略.

关键词: 共价有机框架, 金属有机框架, 自扩散系数, 迁移学习, 分子动力学模拟

The self-diffusion coefficient of gas molecules within metal/covalent organic frameworks (MOFs/COFs) is a critical physicochemical property that profoundly impacts their performance in gas storage, separation, chemical catalysis, and so on. Molecular dynamics (MD) simulation is a primary approach to assessing the self-diffusion of light-gas in nanoporous materials. With the explosive number of nanoporous materials, machine learning-assisted computational screening to accelerate the investigation of self-diffusion and explore their structure-property relationship has attracted much attention. However, the asymmetric development of the database between MOFs and other nanoporous materials (such as COFs) led to a data imbalance that challenged the development of machine learning for other porous materials, especially for computation-ready experimental (CoRE) databases. Meanwhile, transfer learning (TL) can mitigate such a challenge to enhance generalization by importing similar information extracted from a well-established database (such as CoRE MOFs). This study employs molecular dynamics simulations to predict the self-diffusion coefficients of eight light gases (H₂, CH₄, H₂S, CO₂, N₂, C₂H₆, C₃H₈, C₄H₁₀) in the CoRE MOF database and five light gases (H₂, CH₄, H₂S, CO₂, N₂) in the CoRE COF database. By utilizing the descriptor obtained from the nanoporous structure and the gas molecule, three ensemble-based and network-based transfer learning algorithms were trained. In detail, there are seven geometric descriptors obtained from the structure, including the largest cavity diameter (LCD), pore limiting diameter (PLD), largest free path diameter (LFPD), density (ρ), unit cell, void fraction (VF) and pore volume (PV), and four chemical descriptors obtained from light gas, including kinetic dynamic (Dia), quadrupole moment (Qua), polarizability (Pol) and dipole moment (Dip). The Two-Stage TrAdaBoost.R2 algorithm is adopted to adjust the parameter for the ensemble model for transfer learning, whereas the fine-tuning strategy is performed for the neural network for TL. Among them, the light gradient boosting machine (LGBM) was identified as a promising transfer learning model for high-accuracy (R²=0.802) prediction of the self-diffusion. The kinetic diameter, polarizability of gas molecule, and pore limiting diameter of nanoporous structure are emerging as dominant descriptors with relative importance is 14%, 14%, and 12%, in which small Dia, Pol, and large PLD benefit the diffusion. Furthermore, the transfer learning LGBM model can predict the self-diffusion of three types of gas (C₂H₆, C₃H₈, C₄H₁₀) with a Spearman's correlation coefficient (SRCC) equal to 0.821. This work validates the feasibility of transfer learning-assisted high-throughput screening, offering a feasible approach for deep learning and cross-material studies of nanoporous materials under data scarcity constraints.

Key words: covalent-organic frameworks, metal-organic frameworks, self-diffusion coefficient, transfer learning, molecular dynamics simulation

引用此文

彭天资, 沈嘉克, 郭淑雅, 夏潇潇, 李炜. 迁移学习预测金属/共价有机骨架材料内小分子气体自扩散系数研究[J]. 化学学报, 2026, 84(3): 305-315.

Peng Tianzi, Shen Jiake, Guo Shuya, Xia Xiaoxiao, Li Wei. Transfer Learning Predicted the Self-Diffusion Coefficients of Light-Gas in Metal/Covalent Organic Frameworks[J]. Acta Chimica Sinica, 2026, 84(3): 305-315.

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图/表 10

Descriptors	Abbreviations	Units
Largest Cavity Diameter	LCD	nm
Pore Limiting Diameter	PLD	nm
Largest Free Path Diameter	LFPD	nm
Framework Density	ρ	g•cm⁻³
Unit Cell Volume	PV(1)	nm³
Porosity	PV(2)	—
Pore Volume per Unit Mass	PV(3)	cm³•g⁻¹
Kinetic Diameter	Dia	nm
Polarizability	Pol	nm³
Quadrupole Moment	Qua	C•m²
Dipole Moment	Dip	D

表1. 描述符及其缩写和单位列表

Table 1. List of descriptors, their abbreviations, and units

图1. MOFs迁移学习预测COFs内小分子气体自扩散系数流程图

Figure 1. The flowchart of transfer learning based on MOF datasets to predict the self-diffusion of light-gas in the COFs dataset

图2. 数据集的t-SNE分布图 (a)~(d)依次分别为总数据集、总数据集以气体区分, MOFs数据集、COFs数据集的t-SNE分布图, 其中(a)、(c)和(d)以log(PLD)着色

Figure 2. t-SNE Distribution of MOF and COF Datasets t-SNE distribution plots of datasets, Panels (a)~(d) correspond to the entire dataset, the entire dataset divided by gas molecule, the MOFs dataset, and the COFs dataset, which (a), (c), and (d) are colored by the log(PLD), respectively

图3. 几何描述符与自扩散系数的构效关系 (a)~(g)依次分别为LCD、PLD、LFPD、ρ、PV(1)、PV(2)、PV(3)与各类气体分子自扩散系数对数值的散点图, 其中主图中的是COFs, 小图中的是MOFs, 气体分子的种类由散点的形状和颜色区分

Figure 3. Structure-property relationships of geometric descriptors and self-diffusion coefficients The scatter plots illustrate the relationships between geometric descriptors and the logarithmic self-diffusion coefficient (lgD) of gas molecules in frameworks. Panels (a)~(g) correspond to the largest cavity diameter (LCD), pore limiting diameter (PLD), largest free path diameter (LFPD), framework density (ρ), unitcell volume, void fraction, and unit mass pore volume (PV(1), PV(2), PV(3)), respectively. Main plots represent COFs, with insets showing MOFs. Gas molecule types are distinguished by scatter point shapes and colors

图4. 描述符的Pearson相关系数热图描述符与自扩散系数之间的Pearson相关系数热图, (a)对应MOFs数据集, (b)对应COFs数据集

Figure 4. Pearson correlation heatmap of descriptors Heatmap of Pearson correlation coefficients between descriptors and the self-diffusion coefficient. Panel (a) corresponds to the MOFs dataset, and panel (b) corresponds to the COFs dataset

Model	MOFs			COFs
Model	R²	SRCC	MSE	R²	SRCC	MSE
RF	0.806	0.855	0.051	0.716	0.805	0.091
XGBR	0.813	0.862	0.049	0.666	0.785	0.108
LGBM	0.817	0.863	0.048	0.683	0.792	0.102
DNN	0.792	0.841	0.054	0.669	0.786	0.107

表2. MOFs预训练与COFs直接泛化预测结果

Table 2. MOFs pretraining and COFs direct generalization prediction results

Learning Way	Model	COFs
Learning Way	Model	R²	SRCC	MSE
Direct Learning	RF	0.809	0.852	0.063
	XGBR	0.826	0.866	0.057
	LGBM	0.827	0.866	0.057
	DNN	0.781	0.841	0.072
Transfer Learning	RF	0.775	0.822	0.071
	XGBR	0.791	0.833	0.068
	LGBM	0.803	0.842	0.064
	DNN_1	0.771	0.826	0.074
	DNN_2	0.753	0.819	0.080
	DNN_3	0.760	0.830	0.078

表3. COFs直接学习与迁移学习结果

Table 3. COFs direct learning and transfer learning results

图5. 自扩散系数预测值与模拟值的比较各模型的自扩散系数预测值与模拟值之间的散点图, (a)~(f)依次对应RF、XGBR、LGBM、DNN_1、DNN_2和DNN_3

Figure 5. Comparison of predicted and simulated self-diffusion coefficients Scatter plots of predicted versus simulated self-diffusion coefficients (D) for different models. Panels (a)~(f) correspond to Random Forest (RF), Extreme Gradient Boosting Regression (XGBR), Light Gradient Boosting Machine (LGBM), and three Deep Neural Network models (DNN_1, DNN_2, DNN_3), respectively

图6. 模型的SHAP值解释图 (a)对应LGBM, (b)对应DNN_1, 其各自的左图为SHAP值重要性, 右图为特征密度散点图

Figure 6. SHAP value interpretation of model SHAP value interpretation plots for different models. Panel (a) corresponds to Light Gradient Boosting Machine (LGBM), and panel (b) corresponds to Deep Neural Network (DNN_1). The left plot in each panel shows SHAP value importance, and the right plot shows the feature density scatter plot

图7. (a)迁移学习LGBM模型预测C2H6、C3H8、C4H10三类气体在30种COF结构中的自扩散系数; (b)迁移学习DNN_1模型预测C2H6、C3H8、C4H10三类气体在30种COF结构中的自扩散系数

Figure 7. (a) The transfer learning-based LGBM model predicts the self-diffusion of C2H6, C3H8, and C4H10 among 30 COF structures. (b) The transfer learning-based DNN_1 model predicts the self-diffusion of C2H6, C3H8, and C4H10 among 30 COF structures

参考文献 53

[1]	O'Keeffe M.; Peskov M.A.; Ramsden S.J.; Yaghi O.M.; Acc. Chem. Res. 2008, 41, 1782.
[2]	Zhou H.-C. J.; Kitagawa S. Chem. Soc. Rev. 2014, 43, 5415.
[3]	Gao C.; Zhang S.-T.; Pang H. Acta Chim. Sinica 2025, 83, 962 (in Chinese).
	(高春, 张松涛, 庞欢, 化学学报, 2025, 83, 962.)
[4]	Feng X.; Ding X.; Jiang D. Chem. Soc. Rev. 2012, 41, 6010.
[5]	Furukawa H.; Cordova K. E.; O'Keeffe M.; Yaghi O. M. Science 2013, 341, 974.
[6]	Ding S.-Y.; Wang W. Chem. Soc. Rev. 2013, 42, 548.
[7]	Furukawa H.; Yaghi O. M. J. Am. Chem. Soc. 2009, 131, 8875.
[8]	Makal T. A.; Li J.-R.; Lu W.; Zhou H.-C. Chem. Soc. Rev. 2012, 41, 7761.
[9]	Gong L.; Ye Y.; Liu Y.; Li Y.; Bao Z.; Xiang S.; Zhang Z.; Chen B. ACS Appl. Mater. Interfaces 2022, 14, 19623.
[10]	Wu Z.-L.; Zhang L.; Chen Y.; Li J.-P.; Li L.-B. Acta Chim. Sinica 2025, 83, 917 (in Chinese).
	(吴子林, 张璐, 陈杨, 李晋平, 李立博, 化学学报, 2025, 83, 917.)
[11]	Yan B.; Song J.-H.; Zhang D.-L.; Guan Z.-J.; Fang Y. Chin. J. Chem. 2025, 43, 1078.
[12]	Kalidindi S. B.; Yusenko K.; Fischer R. A. Chem. Commun. 2011, 47, 8506.
[13]	Ma L.; Abney C.; Lin W. Chem. Soc. Rev. 2009, 38, 1248.
[14]	Ban M.-H.; Shuang Y.-Z.; Yang A.-P.; Zheng C.-Y.; Zhang W.; Xu F. Acta Chim. Sinica 2025, 83, 1435 (in Chinese).
	(班渺寒, 双亚洲, 杨安平, 郑长勇, 张伟, 徐飞, 化学学报, 2025, 83, 1435.)
[15]	Li C.-Q.; Yu J.-J.; Feng X. Acta Chim. Sinica 2025, 83, 1223 (in Chinese).
	(李澄秋, 余嘉俊, 冯霄, 化学学报, 2025, 83, 1223.)
[16]	Zhang K.; Wu L.; Zhang Y.; Zhang H.; Wu D. Chin. J. Chem. 2025, 43, 61.
[17]	Cui Y.-Q.; Li J.-Y.; Sun J.-K. Acta Chim. Sinica 2025, 83, 624 (in Chinese).
	(崔雨琪, 李军玉, 孙建科, 化学学报, 2025, 83, 624.)
[18]	Luo X.; Chen Y.; Lin J.-T.; Luo J.; Xia R.-Q.; Yin N.; Lin Y.-M.; Duan H.; Ren S.-B.; Gao Q.; Ning G.-H.; Li D. Chin. J. Chem. 2025, 43, 1199.
[19]	Mu W.; Liu D.-H.; Yang Q.-Y.; Zhong C.-L. Acta Phys.-Chim. Sin. 2010, 26, 1657 (in Chinese).
	(穆韡, 刘大欢, 阳庆元, 仲崇立, 物理化学学报, 2010, 26, 1657.)
[20]	Walenszus F.; Bon V.; Evans J. D.; Kaskel S.; Dvoyashkin M. J. Phys. Chem. Lett. 2020, 11, 9696.
[21]	Chen H.; Snurr R. Q. Langmuir 2020, 36, 1372.
[22]	Borah B.; Zhang H.; Snurr R. Q. Chem. Eng. Sci. 2015, 124, 135.
[23]	Qin Y.; Han X.; Li Y.; Han A.; Liu W.; Xu H.; Liu J. ACS Catal. 2020, 10, 5973.
[24]	Gao Z.; Wang H.; Qu Z.-G. J. Ind. Eng. Chem. 2025, 76, 4259 (in Chinese).
	(高正, 汪辉, 屈治国, 化工学报, 2025, 76, 4259.)
[25]	Liu Z.-L.; Li W.; Liu H.; Zhuang X.-D.; Li S. Acta Chim. Sinica 2019, 77, 323 (in Chinese).
	(刘治鲁, 李炜, 刘昊, 庄旭东, 李松, 化学学报, 2019, 77, 323.)
[26]	Li W.; Liang T.-G.; Lin Y.-C.; Wu W.-X.; Li S. Prog. Chem. 2022, 34, 2619 (in Chinese).
	(李炜, 梁添贵, 林元创, 吴伟雄, 李松, 化学进展, 2022, 34, 2619.)
[27]	Wang S.-H.; Xue X.-Y.; Cheng M.; Chen S.-C.; Liu C.; Zhou L.; Bi K.-X.; Ji X. Acta Chim. Sinica 2022, 80, 614 (in Chinese).
	(王诗慧, 薛小雨, 程敏, 陈少臣, 刘冲, 周利, 毕可鑫, 吉旭, 化学学报, 2022, 80, 614.)
[28]	Ren E.; Coudert F.-X. J. Phys. Chem. C 2024, 128, 6917.
[29]	Guo S.; Huang X.; Situ Y.; Huang Q.; Guan K.; Huang J.; Wang W.; Bai X.; Liu Z.; Wu Y.; Qiao Z. Adv. Sci. 2023, 10, 2301461.
[30]	Li W.; Cai Z.-L.; Li S.; Wu W.-X. Sep. Purif. Technol. 2025, 378, 134533.
[31]	Park J.; Kim H.; Kang Y.; Lim Y.; Kim J. JACS Au 2024, 4, 3727.
[32]	Zhuang F.; Qi Z.; Duan K.; Xi D.; Zhu Y.; Zhu H.; Xiong H.; He Q. P IEEE 2021, 109, 43.
[33]	Park H.; Kang Y.; Kim J. ACS Appl. Mater. Interfaces 2023, 15, 56375.
[34]	Zhao G.; Brabson L. M.; Chheda S.; Huang J.; Kim H.; Liu K.; Mochida K.; Pham T. D.; Prerna; Terrones G. G.; Yoon S.; Zoubritzky L.; Coudert F.-X.; Haranczyk M.; Kulik H. J.; Moosavi S. M.; Sholl D. S.; Siepmann J. I.; Snurr R. Q.; Chung Y. G. Matter 2025, 8, 102140.
[35]	Tong M.; Lan Y.; Yang Q.; Zhong C. Chem. Eng. Sci. 2017, 168, 456.
[36]	Rappe A. K.; Casewit C. J.; Colwell K. S.; Goddard W. A., III; Skiff W. M. J. Am. Chem. Soc. 1992, 114, 10024.
[37]	Chen B.; Potoff J. J.; Siepmann J. I. J. Phys. Chem. B 2001, 105, 3093.
[38]	Dubbeldam D.; Calero S.; Ellis D. E.; Snurr R. Q. Mol. Simul. 2015, 42, 81.
[39]	Wilmer C. E.; Leaf M.; Lee C. Y.; Farha O. K.; Hauser B. G.; Hupp J. T.; Snurr R. Q. Nature Chem. 2012, 4, 83.
[40]	Demir H.; Keskin S. Mol. Syst. Des. Eng. 2021, 6, 627.
[41]	Han C.; Verploegh R. J.; Sholl D. S. J. Phys. Chem. Lett. 2018, 9, 4037.
[42]	Sung I. T.; Cheng Y.-H.; Hsieh C.-M.; Lin L.-C. Ind. Eng. Chem. Res. 2025, 64, 1859.
[43]	Willems T. F.; Rycroft C.; Kazi M.; Meza J. C.; Haranczyk M. Microporous Mesoporous Mater. 2012, 149, 134.
[44]	Ozer D. J. Psychol. Bull. 1985, 97, 307.
[45]	Hodson T. O. Geosci. Model Dev. 2022, 15, 548.
[46]	Wissler C. Science (New York, N.Y.). 1905, 22, 309.
[47]	Al-Stouhi S.; Reddy C. K. In Machine Learning and Knowledge Discovery in Databases, Lecture Notes in Computer Science 6911, Eds.: Gunopulos,D.; HofmannT.; MalerbaD.; VazirgiannisM.,Springer, Berlin, Heidelberg, 2011, pp. 60-75.
[48]	Anderson G. W.; Castano D. J. Phys. Lett. B 1995, 347, 300.
[49]	Cai T. T.; Ma R. J. Mach. Learn. Res. 2022, 23, 1.
[50]	Chen S.-C.; Cheng M.; Wang S.-H.; Wu J.-K.; Luo L.; Xue X.-Y.; Ji X.; Zhang C.-C.; Zhou L. Chem. J. Chinese U. 2023, 44, 1 (in Chinese).
	(陈少臣, 程敏, 王诗慧, 吴金奎, 罗磊, 薛小雨, 吉旭, 张长春, 周利, 高等学校化学学报, 2023, 44, 1.)
[51]	Qiao Z.; Peng C.; Zhou J.; Jiang J. J. Mater. Chem. A 2016, 4, 15904.
[52]	Guan Y.; Huang X.; Xu F.; Wang W.; Li H.; Gong L.; Zhao Y.; Guo S.; Liang H.; Qiao Z. Nanomaterials 2024, 14, 1074.
[53]	Cai Z.; Li W.; Chung Y. G.; Li S.; Liang T.; Wu T. Sep. Purif. Technol. 2024, 348, 127752.