Organic light-emitting diodes (OLEDs) are a potent candidate for augmented reality (AR) and virtual reality (VR) displays. However, OLED outcoupling efficiency still poses a significant challenge in mass production. Surface plasmon polaritons (SPPs) cause about 30% optical loss in OLEDs, absorbing photon energy at the interface between the dielectric and the anode metal. In this study, we focused on exciting SPPs using a two-dimensional (2D) hole-arrayed double-anode structure with the top anode, the interlayer, and the bottom anode. We defined the functions of the three components and optimized the design parameters for maximum outcoupling efficiency of OLEDs using the finite-difference time-domain (FDTD) method. The 2D hole-arrayed double-anode excites SPPs of the top anode and induces SPPs in the bottom anode. The bottom anode couples (and reflects) with SPPs of the top and bottom anodes. A key design rule of our structure is the diameter of the 2D hole array on the top anode that is determined at maximizing phase matching with SPPs of the top and bottom anodes for the outcoupling enhancement factor for OLED outcoupling efficiency. The thickness of the interlayer is smaller than the skin depth of the top anode metal. The thickness of the bottom anode is greater than 30 nm, providing over 89% reflectance at the SPP wavelength. Consequently, we enhanced the outcoupling efficiency to 1.58 folds more than that of conventional top-emission OLEDs (TE-OLEDs). Further, we developed the model to predict the outcoupling enhancement factor via input structural parameters using linear regression, XGB Regressor, and MLP (statistical, machine learning, and deep learning models, respectively), with 89.4% accuracy in the mean absolute error (MAE). We hope that our new approach promotes future studies on SPP excitation for optical devices.