Polymer electrolyte membrane water electrolyzers (PEMWEs) are electrochemical devices that can be used for the production of hydrogen. In a PEMWE the anode is the most complex electrode to study due to the high overpotential of the oxygen evolution reaction (OER), not widely understood. A physical bottom-up multi-scale transient model describing the operation of a PEMWE anode is proposed here. This model includes a detailed description of the elementary OER kinetics in the anode, a description of the non-equilibrium behavior of the nanoscale catalyst-electrolyte interface, and a microstructural-resolved description of the transport of charges and O(2) at the micro and mesoscales along the whole anode. The impact of different catalyst materials on the performance of the PEMWE anode, and a study of sensitivity to the operation conditions are evaluated from numerical simulations and the results are discussed in comparison with experimental data.