Physics-informed and machine learning-based design optimization of Solid Oxide Fuel Cells

This paper presents a two-phase approach towards a multiphysics and constrained multiobjective design optimization of a solid oxide fuel cell (SOFC) system. The first phase of the proposed approach uses a directly coupled multiphysics model (including electrochemistry, thermal, and fluid physics submodels) with a heuristic algorithm to determine the effects of the design variables on the performance of the SOFC system for extensive combinations of the design variables. In the second phase, four machine learning (ML) models are developed for regression purposes. The ML models include ensemble regression (ER), Gaussian process regression (GPR), support vector machine regression (SVMR), and neural network regression (NNR). The ML models are trained using data generated from extensive multiphysics simulations. The trained ML models are subsequently integrated within a constrained multiobjective optimization algorithm to determine optimal values of the design parameters for the SOFC system. The design variables for both phases include the physical geometry of the SOFC, as well as the fuel and air velocities. The optimization objectives include minimizing the temperature gradient, minimizing the cost per unit Watt as well as maximizing the power density of the SOFC. The Pareto Optimal Solutions (POS) obtained using this approach were evaluated to benefit future SOFC design efforts. The results show very good performance of the trained ML models in predicting the proposed objectives from the SOFC. For this application, the NNR and GPR models performed somewhat better than the EF and SVMR models. The NNR's normalized RMSE values for predicting the temperature gradient, power density and cost per unit watt are 0.0423 °C, 0.007W/cm² and $0.0126/W respectively while that of GPR is predicting the same parameters are 0.0415 °C, 0.0052W/cm² and $0.013/W respectively. The POS solutions present valuable information to SOFC designers regarding trade-offs in optimizing the geometry and operation of SOFC systems.