Learning-augmented model predictive control for energy management in hydrogen-battery hybrid trains: A comparative deep learning study

To decarbonize non-electrified rail networks, hydrogen-battery hybrid trains are emerging as promising alternatives to diesel traction. In such hybrid propulsion, the energy management system dynamically allocates power between the fuel cell and battery, making control design critical for hydrogen economy, charge sustainability, and component protection. Model predictive control combined with demand forecasting is a promising strategy, yet most prior studies adopt a single learning architecture and do not systematically assess how predictor choice affects closed-loop performance. This study presents a controlled comparison of four deep learning architectures: Long Short-Term Memory, Gated Recurrent Unit, One-Dimensional Convolutional Neural Network, and Echo State Network, as power-demand predictors within a unified model predictive control framework for hydrogentrain energy management. The control layer uses a zero-dimensional drivetrain model incorporating train dynamics, powertrain behavior, the fuel cell stack, and the battery system. The framework is developed using data from ALSTOM’s Coradia Stream H train on the Brescia-Iseo-Edolo line and validated on two additional routes. Results reveal architecture-specific closed-loop trade-offs relative to standard model predictive control. The Echo State Network achieves the lowest prediction error and the smallest mean state-of-charge deviation, about 2.4%. Long Short-Term Memory yields the largest reductions in fuel-cell and battery loading stress, by 4.5 MW and 36.5 MW, respectively. Gated Recurrent Unit provides the highest hydrogen savings, up to 13.4%, with strong crossroute generalization, whereas the One-Dimensional Convolutional Neural Network overfits the training route