Modeling and machine learning driven optimization of performance of CeO₂–TiC-enhanced nafion membranes in PEMFC

This study presents a modeling and machine learning framework for the optimal design of a novel proton exchange membrane fuel cell (PEMFC) incorporating Nafion/CeO₂–TiC hybrid membranes, aimed at enhancing performance and durability. In the first part, using experimental data, a semi-empirical model is developed, integrating electrochemical fundamentals with empirical equations to describe water content, conductivity, and hydrogen crossover.A machine-learning model is trained to predict power density, total efficiency, and hydrogen crossover across broad operating conditions and membrane compositions. The training set consists of Nafion 212, recast Nafion, and CeO2–TiC/Nafion membranes with 0.5–2.0 wt% filler, augmented by Monte Carlo–synthesized operating points to offset limited experiments.The trained neural network is embedded in a MILP via piecewise-linear ReLU constraints, enabling multi-objective design optimization that quantifies trade-offs among power density, efficiency, and hydrogen crossover. Optimal CeO₂–TiC loading is condition-dependent, and is obtained at 90 °C and 100% RH, 2.0 wt% which corresponds to 0.252 W cm−2 power density, 51.66% efficiency, and ∼1.16 × 10−8 mol cm−2 s−1 H₂ crossover. Higher filler loading is favored at elevated temperature and humidity, while lower loadings are suitable for low temperature or low humid conditions.