Combining physical modeling and machine learning for micro-scale modeling of a fuel cell electrode

Abstract Microscale modeling plays a critical role in fuel cell development, offering deep insights into the microscale transport phenomena and electrochemical reactions. This level of detail is essential for optimizing the performance of a single fuel cell, enabling the precise design and improvement of materials and structures at the microscale and consequently enhancing the overall efficiency of a stack. Here, we show a comprehensive transition from white-box models, characterized by their reliance on physical laws, to black-box models exemplified by neural networks, which excel in pattern recognition from provided data without necessitating a clear understanding of the underlying processes. This spectrum encompasses the inherent challenges and merits of both methodologies. While white-box models are recognized for their reliability due to their foundation in mathematical equations that describe physical phenomena, they often require the integration of empirical parameters and are susceptible to experimental errors, much like their black-box counterparts. The core novelty in this study lies in the synergistic integration of these two paradigms, specifically tailored for enhancing the predictive accuracy in solid oxide fuel cell modeling. In this approach, the neural network is employed to replace different parts of the mathematical model, from refining empirical parameters in the electrochemical model to replacing the entire electrochemical model. The adjustment of parameters is conducted by an evolutionary strategy based on the outputs of the mathematical model. The results underscore the superiority of the gray box in achieving higher prediction accuracy and in minimizing the requisite data volume for network training. This presented approach not only bridges the gap between the deterministic clarity of white-box models and the data-driven insights of black-box models but also strategically distributes the computational load between them, thereby offering a promising solution to the prevalent challenges in solid oxide fuel cell modeling.