Electrified propulsion systems with hydrogen-fueled fuel cells can potentially reduce carbon dioxide emissions from aircraft. However, achieving a substantial increase in the gravimetric/volumetric power density of fuel cell systems poses a considerable challenge. In this study, we focus on high temperature polymer electrolyte membrane fuel cells (HT-PEMFCs) working between 100 and 200°C. To design an optimized PEMFC structure for an electric aircraft, we have developed a numerical model that employs the finite element method (FEM) (COMSOL Multiphysics) to couple electrochemistry, gas diffusive and convective transports, and heat transfer in fuel cell components such as separators, gas flow channels, gas diffusion layers, catalyst layers, and a PEM. We thereby derive the current distributions associated with three-dimensional hydrogen, oxygen, and water vapor concentration distributions, as well as temperature distributions. Moreover, we develop a machine learning model from the data outputs of the FEM model, which serves as training data, to reduce the computational costs for the fuel cell stack design incorporated in a system-level numerical model.