Prediction of Methane Adsorption Isotherms in Metal–Organic Frameworks by Neural Networks: Two-Dimensional Energy Gradient Feature and Masked Learning Mechanism

Metal-organic frameworks (MOFs) have shown great application potential in the field of energy gas storage and separation due to their unique tunable porosity and pore environment. Accurate prediction of the methane adsorption isotherms of MOF materials at different temperatures is crucial for optimizing and designing their methane storage and separation processes. In this work, we proposed a novel multioutput neural network (NN) model for rapidly predicting CH₄ adsorption isotherms in a large number of MOFs at different temperatures. The model can be trained using a masked learning mechanism, with inputs such as two-dimensional energy gradient feature (2D-EGF) descriptors, geometrical property descriptors and chemical information descriptors of MOFs. Initially, the methane adsorption isotherms for 17,644 MOFs materials at various temperatures (278-338 K) were calculated using classical density functional theory (cDFT), and the parameters of the extended Langmuir equation (3P and 4P) were obtained through nonlinear fitting. The entire data set, comprising 64,092 samples, was split into a training set and a test set at a ratio of 8:2 for the purpose of training and validating a neural network model. The model was constructed with multiple outputs, including methane adsorption capacities at 21 pressure points and the parameters of the extended Langmuir equation (3P and 4P). The results show that both the 4P and 3P models achieve the optimal prediction accuracy when the unmasked probability parameter <i>p</i> was set to 0.6. The SHAP values analysis demonstrates that the geometrical features exhibit the most significant impact on the targets at all pressures, except for temperature variation (TK). The models' transferability was evaluated by comparing their prediction accuracy across three additional scenarios: unseen MOFs at the same temperature, seen MOFs at extended temperatures, and experimental MOFs at room temperature. The model can accurately predict the methane adsorption isotherms of unseen hypothetical MOFs under the same temperature conditions. Additionally, the models' predictions of the methane adsorption isotherms for known MOFs at extended temperatures (268 and 358 K) are essentially consistent with the results of cDFT simulations. However, the model still exhibits significant deviations in its prediction of the methane adsorption isotherms in four experimental MOFs at room temperature when compared to the experimental data. The neural network approach is expected to act as a versatile and precise tool for predicting gas adsorption equilibrium data in MOFs, which is crucial for significant gas separation processes.