Predicting CO₂ adsorption in Cu- and Zn-metal-organic frameworks using a permutation-invariant deep learning framework

A deep-learning framework that predicts CO 2 uptake in Metal-organic frameworks (MOFs) has been proposed. MOFs are promising material adsorbents for carbon dioxide (CO 2 ) capture due to their tunable porosity and surface chemistry. However, their wide range of structural variation rendering experimental screening laborious if not impractical. The proposed framework combines string-based chemical descriptors (SMILES and SELFIES, with one-hot and ordinal encodings) with physical descriptors (pore-limiting diameter, largest cavity diameter, gravimetric and volumetric surface areas, void fraction, topology, and catenation), and incorporating a permutation-invariant aggregator over multiple MOFs linkers. Three deep learning architectures: Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM) were trained and evaluated on the Cu-MOF and Zn-MOF subsets of the MOFX-DB database. The statistical differences in predictive accuracy were assessed using the Diebold–Mariano (DM) test. Chemical descriptors alone yielded coefficient of determination R² below 14% because three-dimensional structural information is lost in string encodings but combining SMILES one-hot encoding with physical descriptors increased R² to 87.07–87.90% for Cu-MOF and 83.50–83.61% for Zn-MOF, with the permutation-invariant aggregator contributing significant improvement gains (from 1% up to 14%). DM testing showed that, for Cu-MOF, the three architectures are statistically equivalent, whereas for Zn-MOF MLP and CNN significantly outperformed LSTM. Training on a combined multi-pressure dataset (0.01–2.5 bar) further improved performance to R² ≥ 0.976. Case-study isotherm reconstructions of hMOF structures yielded R² = 0.9927 for a Cu-MOF (hMOF-5077787) and R² = 0.9991 with average relative errors below 3% above 0.05 bar for Zn-MOF. The results demonstrated the proposed framework application as a rapid screening tool across realistic operating conditions for post-combustion CO 2 capture.