Gas-Conditioned Message Passing Graph Neural Network for Permeability Prediction in Polymeric Membranes

Abstract

Designing polymeric membranes for diverse gas-separation applications remains a critical challenge. Machine learning (ML) models can significantly accelerate this effort by capturing complex relationships between polymer-gas pairs and enabling permeability prediction over an extended chemical space of gases and polymers. In this work, we present a novel ML framework, the gas-conditioned message passing neural network (GC-MPNN), that jointly combines gas descriptors and polymer chemistry in a fused neural network model. Polymers are represented at the monomer level and encoded as molecular graphs, where node and edge information is propagated through message-passing layers. Six gas species (He, H2, N2, O2, CH4, and CO2) are represented using multiple descriptor sets spanning thermodynamic, kinetic, and electrostatic properties, along with one-hot encodings and combined feature sets that include kinetic plus thermodynamic descriptors and the full physicochemical descriptor set. For each descriptor combination, model hyperparameters are optimized using Bayesian optimization within a leave-one-gas-out (LOGO) validation framework. Test performance is then evaluated on the gas species excluded entirely from the corresponding training fold (out-of-training set) and compared across descriptor sets. For most gas species, the model achieves strong predictive performance (R2 ∼ 0.86–0.96), while CO2 remains more challenging in terms of absolute prediction accuracy (R2 ∼ 0.44). Active learning sampling further improves model performance by adding a few labeled samples from the test gas species into the training set. Among the three strategies tested, deep ensemble-based sampling and random sampling show strong improvement, with R2 reaching approximately ∼ 0.95 for all gas species, while evidential regression shows less consistent improvement. The model is further evaluated on a smaller polymer-gas dataset containing hydrocarbon species (C2H4, C2H6, C3H6, C3H8, and n-C4H10) using the GC-MPNN trained only on the six base gases, achieving moderate to strong Pearson correlations (r ∼ 0.77–0.89) for these out-of-training gases. Overall, this work presents a machine learning model that can learn transferable polymer-gas relationships from known gas species and extend them to previously unseen gases.