Transfer Learning Predicted the Self-Diffusion Coefficients of Light-Gas in Metal/Covalent Organic Frameworks

doi:10.6023/A25110385

Abstract

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

Cite this article

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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Fig. & Tab. 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

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

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

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

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

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

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

Table 3. COFs direct learning and transfer learning results

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

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

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

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