Physics-informed neural modeling of interfacial tension in hydrogen-rich systems using attention-based learning

Underground hydrogen storage (UHS) in geological formations is a critical enabler for large-scale, long-duration energy buffering in hydrogen-centric energy systems. Among the key parameters influencing storage feasibility and operational safety is the interfacial tension (IFT) between hydrogen and brine under subsurface conditions. This study introduces a physics-informed neural network (PINN) model designed to predict IFT across a broad spectrum of temperatures, pressures, brine salinities, and gas compositions, including H₂, CO₂, and CH₄. A comprehensive dataset of experimentally measured IFT values was compiled through an extensive literature survey, ensuring robust thermodynamic coverage. The model integrates domain knowledge into the learning architecture by embedding thermodynamic relationships and residual-based physical constraints, complemented by attention mechanisms for improved feature representation. The model achieved excellent agreement with experimental observations, with training performance showing R² = 0.9954 and MSE = 0.5128, and testing results yielding R² = 0.9716 and MSE = 5.1924, corresponding to average prediction errors below 1 %. To quantify predictive uncertainty, Monte Carlo dropout was employed, enabling the estimation of epistemic uncertainty and highlighting regions of sparse data or extrapolation risk. SHAP (SHapley Additive exPlanations) analysis revealed that temperature is the most influential factor governing IFT, followed by brine salinity, with gas composition introducing nonlinear effects. The resulting IFT surface successfully captures transitions between thermodynamic regimes, reflecting coupled effects of phase behavior, ionic strength, and gas solubility. Residual diagnostics confirmed strong physical consistency, with deviations from embedded constraints remaining below 1.2 % even under extreme conditions. This work demonstrates the efficacy of physics-guided machine learning in modeling interfacial phenomena relevant to subsurface hydrogen storage and offers a reliable, interpretable framework to support the design, risk assessment, and optimization of UHS systems in saline aquifers and other geological formations.