A quantitative structured design guidance for porous solid oxide fuel cell cathodes via multiphysics complexity reduction

Designing complex physical systems governed by strongly coupled and non-linear parameters is a persistent challenge in materials science and engineering, often addressed through either extensive experimental campaigns or computationally demanding optimisation techniques. However, comprehensive end-to-end workflows that quantitatively integrate established analysis techniques to support performance-oriented design remain limited. In the specific case of porous mixed ionic electronic conductor (MIEC) cathodes for solid oxide fuel cells (SOFCs), existing studies typically focus on optimising isolated material, kinetic, or microstructural properties, without providing an integrated framework that quantitatively links design parameters to overall electrochemical performance. In this work, we introduce a structured and modular design workflow that integrates established tools for local and global sensitivity analysis through uncertainty quantification, complemented by intuitive data visualisation tools. For a posteriori validation of design choices, dimensionality reduction is achieved through partial least squares methods implemented with kernel ridge regression, allowing non-linear system behaviour to be retained. The proposed framework is applied to a porous MIEC cathode for SOFC applications, described by a one-dimensional physics-based model. The analysis identifies the parameters that exert the greatest influence on performance in terms of current density, area specific resistance and thickness utilisation. The MIEC solid volume fraction and material doping fraction emerge as the dominant factors governing cathode thickness utilisation and cell current density, respectively, followed by kinetic parameters such as the kinetic symmetry coefficient and the surface coverage of adsorbed oxygen. These quantitative insights define a clear hierarchy of influence of microstructural, surface, kinetic and bulk parameters, providing a rational basis for design choices, recommended strategies, and future investigation priorities.