Green hydrogen plays an essential role in decarbonization, with capacity projected to scale to 560 GW by 2030 (vs. 1.39 GW in 2023) in net-zero settings. Proton exchange membrane (PEM) electrolysis is one of the most promising technology routes to green hydrogen production, and real-time system health monitoring of PEM electrolyzers is essential for their scalable deployment. In lab settings, performance degradation can be characterized through electrochemical testing protocols by periodic pauses of normal operation. Such interruption is not practical for full-scale stack deployments, limiting system operators' ability to make real-time assessments of state-of-health (SoH). We present a machine learning (ML) framework that performs virtual electrochemical characterization during normal operation. The method uses an encoder-decoder transformer, conditioned on operational data, to reconstruct characterization outputs, focusing here on polarization curves. Inspired by patch-based sequence tokenization, we segment the inputs into patches and encode them to form meaningful tokens, which substantially improves learning efficiency. Across four longitudinal runs, lasting up to 478 hours on different test cells and loading cycles, the model accurately reconstructed polarization curves and achieved 10x reduction in mean squared error (MSE) compared to a vanilla transformer. This proof-of-concept demonstrates that ML models can enable continuous performance monitoring for PEM electrolyzers and that the encoder captures meaningful latent representations of SoH, opening up opportunities to derive interpretable indicators in future work.