  In this study, we propose to adopt a novel framework, Knowledge-integrated
Machine Learning, for advancing Proton Exchange Membrane Water Electrolysis
(PEMWE) development. Given the significance of PEMWE in green hydrogen
production and the inherent challenges in optimizing its performance, our
framework aims to meld data-driven models with domain-specific insights
systematically to address the domain challenges. We first identify the
uncertainties originating from data acquisition conditions, data-driven model
mechanisms, and domain expertise, highlighting their complementary
characteristics in carrying information from different perspectives. Building
upon this foundation, we showcase how to adeptly decompose knowledge and
extract unique information to contribute to the data augmentation, modeling
process, and knowledge discovery. We demonstrate a hierarchical three-level
framework, termed the "Ladder of Knowledge-integrated Machine Learning", in the
PEMWE context, applying it to three case studies within a context of cell
degradation analysis to affirm its efficacy in interpolation, extrapolation,
and information representation. This research lays the groundwork for more
knowledge-informed enhancements in ML applications in engineering.
