A machine learning driven 3D+1D model for efficient characterization of proton exchange membrane fuel cells

The computational demands of 3D continuum models for proton exchange membrane fuel cells remain substantial. One prevalent approach is the hierarchical model combining a 2D/3D flow field with a 1D sub-model for the catalyst layers and membrane. However, existing studies often simplify the 1D domain to a linearized 0D lumped model, potentially resulting in significant errors at high loads. In this study, we present a computationally efficient neural network driven 3D+1D model for proton exchange membrane fuel cells. The 3D sub-model captures transport in the gas channels and gas diffusion layers and is coupled with a 1D electrochemical sub-model for microporous layers, membrane, and catalyst layers. To reduce computational intensity of the full 1D description, a neural network surrogates the 1D electrochemical sub-model for coupling with the 3D domain. Trained by model-generated large synthetic datasets, the neural network achieves root mean square errors of less than 0.2%. The model is validated against experimental results under various relative humidities. It is then employed to investigate the nonlinear distribution of internal states under different operating conditions. With the neural network operating at 0.5% of the computing cost of the 1D sub-model, the hybrid model preserves a detailed and nonlinear representation of the internal fuel cell states while maintaining computational costs comparable to conventional 3D+0D models. The presented hybrid data-driven and physical modeling framework offers high accuracy and computing speed across a broad spectrum of operating conditions, potentially aiding the rapid optimization of both the membrane electrode assembly and the gas channel geometry.