This study investigates the use of Gaussian Process Regression (GPR) to predict key mechanical properties of porous materials with randomly distributed voids. Understanding the mechanical behavior of these materials is challenging due to the complex influence of void size, spatial distribution, and loading conditions. We developed a GPR model to predict three critical properties: yield stress, strain at failure, and stress at failure for 2D representative volume elements (RVEs) under plane stress conditions. The model was trained using data from simulations with varying void parameters including porosity, spatial distribution, and size distribution (characterized by log-scale distribution parameters). Multiple stress ratios were considered to examine the effect of loading triaxiality. Our results demonstrate that the GPR model achieves high accuracy in predicting both stress and strain at failure, with prediction errors typically below 7\%. However, yield stress prediction proved significantly more challenging, due to substantial overlap in the distribution of yield stresses across different parameter combinations. This overlap suggests an inherent physical limitation in how uniquely yield behavior can be determined from void characteristics alone. The successful prediction of failure properties has practical applications in assessing material performance limits and setting design allowables for additively manufactured materials, where porosity is inherent to the manufacturing process. Current work is focused on extending this study to 3D conditions, which will hopefully lead to the generalization of ductile damage models. This extension aims to incorporate void size and spatial distribution parameters rather than relying solely on scalar porosity, potentially improving the predictive capabilities for complex heterogeneous materials. We note that the surrogate model is not to be viewed as the ultimate goal, but rather as a tool through which to understand and refine the understanding and analytical models that describe the effect of porosity statistics on the ductile fracture process.