Continuum-scale population balance models provide a physically consistent description of catalyst degradation in proton exchange membrane fuel cells (PEMFCs) by resolving the time evolution of particle size distributions. In particular, core-shell Pt-Co catalyst degradation can be modeled using transport type population balance equations defined over particle core radius and shell thickness. While these models accurately capture key degradation mechanisms such as dissolution, redeposition, and coarsening, their high computational cost limits their use in parametric studies, lifetime prediction, and real-time assessment. In this work, we develop non-intrusive reduced order surrogate models for efficient prediction of core-shell Pt-Co catalyst degradation under realistic operating conditions. High-fidelity continuum simulations of the population balance equations are first used to construct a compact Proper Orthogonal Decomposition (POD) basis that captures the dominant morphological evolution of the catalyst population. The time and parameter dependent dynamics of the reduced coefficients are then approximated using neural network based regression models. Two surrogate formulations are investigated: (i) a purely data-driven POD based neural surrogate trained on high-fidelity simulation data, and (ii) a physically regularized variant augmented with weak physics based constraints. These regularization terms encode qualitative degradation behavior, including irreversible loss of active material, smooth temporal evolution, and accelerated degradation at elevated temperatures, without explicitly enforcing the governing partial differential equations. Both surrogate models provide accurate predictions of time dependent degradation trajectories, including the evolution of particle size distributions and derived degradation metrics such as mean particle size and electrochemically active surface area. When compared against the high-fidelity continuum model, the surrogates achieve mean relative Frobenius and L² errors below $5\%$ across a wide range of voltages and temperatures. Inference times are reduced by up to three orders of magnitude relative to direct continuum simulations. The physically regularized surrogate further improves stability and robustness under aggressive operating conditions. These results demonstrate that POD-based neural surrogates provide fast and accurate alternatives to continuum population balance models, enabling efficient parametric