Insights gained from the modal analysis are invoked for predictive large-eddy simulation (LES) wall modeling. Specifically, we employ the first Proper Orthogonal Decomposition (POD) mode in a 2D turbulent channel to augment the law of the wall (LoW). The constructed wall model contains two modes, i.e., the LoW mode and the POD mode, and requires LES information at two matching locations to solve the wall-shear stress. The model protects the LoW like the equilibrium wall model. A-priori tests show that the two modes, i.e., the LoW mode and the POD mode, yield a close approximation of the mean flow in flows with adverse and transverse pressure gradients. A-posteriori tests show that the POD-augmented wall model captures the initial decrease and the rapid decrease of the streamwise wall-shear stress in channels subjected to suddenly imposed adverse and transverse pressure gradients. The resulting model is straight-forward to implement, compatible with high-order codes, and most importantly, accounts for non-equilibrium effects at minimum additional computational cost (compared to the algebraic equilibrium wall model).