In order to predict the complete behavior of complex microstructural materials, one accurate canonical solution is 3D finite element modeling (FEM). This method offers physically accurate predictions for microstructures of high complexity but incurs a large computational cost in doing so. We offer a method for reducing the cost of predicting the mechanical response of one class of microstructural materials, polymer nanocomposites (PNC), enabling fast search and prediction during materials discovery or optimization problems. We constructed a response space of "ground truth" PNC performance by calculating the elastic modulus for PNCs of varying microstructural and constituent property values using 3D FEM. After training of a surrogate model on this set, we found significant time reduction when compared to FEM predictions while still maintaining high accuracy. Predictive strength of the new model was increased further via feature engineering.