Optimization and prediction of power density in proton exchange membrane fuel cells for green energy using advanced machine learning models: a comparative study

This study presents an advanced methodology that integrates experimental validation with machine learning (ML) models to predict and optimize power density in proton exchange membrane fuel cells (PEMFCs). The models considered include Linear Regression (LR), Stepwise Linear Regression (SLR), Tree Regression (TR), Support Vector Machines (SVM), K-Nearest Neighbors (KNN), Gaussian Process Regression (GPR), Neural Networks (NN), Ensemble Learning (ENS), ElasticNet (EL), Random Forest (RF), and Extreme Gradient Boosting (XGBoost). A high-precision experimental setup, employing Nafion 112 membranes, ultra-high-purity gases, and thoroughly controlled operational parameters, generated an extensive data set for model training. Model performance was carefully evaluated using key metrics, including Root Mean Square Error (RMSE), Mean Square Error (MSE), Coefficient of Determination (R²), and Mean Absolute Error (MAE). Among the models tested, GPR and NN demonstrated superior predictive accuracy (RMSE = 32.67 mW cm⁻²; R² = 0.96), capturing nonlinear dependencies in PEMFC dynamics. Residual analysis revealed the models’ ability to predict non-linear dependencies across mid-range operational conditions, while also identifying their limitations under extreme settings, such as high pressure or low current density. Unlike most PEMFC prediction studies that consider only current density and pressure, we explicitly model clamping line load across a wide operating envelope (5–15 N·cm− 1; 5–25 bar). This reveals how compression co-governs gas diffusion and proton conductivity, enabling models that generalize across regimes where flooding, dehydration, and contact resistance jointly shape performance. By integrating data-driven and physics-informed approaches, this research yields nonlinear predictors that provide actionable compression set points to sustain high power density, mitigate degradation risks, and offer indispensable guidelines for designing efficient and robust PEMFC systems, thereby advancing the development of green energy technologies.

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