用物理约束神经网络模拟质子交换膜电解槽膜降解，提升预测准确性和可解释性。

Proton exchange membrane (PEM) electrolyzers are pivotal for sustainable hydrogen production, yet their long-term performance is hindered by membrane degradation, which poses reliability and safety challenges. Therefore, accurate modeling of this degradation is essential for optimizing durability and performance. To address these concerns, traditional physics-based models have been developed, offering interpretability but requiring numerous parameters that are often difficult to measure and calibrate. Conversely, data-driven approaches, such as machine learning, offer flexibility but may lack physical consistency and generalizability. To address these limitations, this study presents the first application of Physics-Informed Neural Networks (PINNs) to model membrane degradation in PEM electrolyzers. The proposed PINN framework couples two ordinary differential equations, one modeling membrane thinning via a first-order degradation law and another governing the time evolution of the cell voltage under membrane degradation. Results demonstrate that the PINN accurately captures the long-term system's degradation dynamics while preserving physical interpretability with limited noisy data. Consequently, this work introduces a novel hybrid modeling approach for estimating and understanding membrane degradation mechanisms in PEM electrolyzers, offering a foundation for more robust predictive tools in electrochemical system diagnostics.