The Fontan procedure is the definitive palliation for pediatric patients born with single ventricles. Surgical planning for the Fontan procedure has emerged as a promising vehicle toward optimizing outcomes, where pre-operative measurements are used prospectively as post-operative boundary conditions for simulation. Nevertheless, actual post-operative measurements can be very different from pre-operative states, which raises questions for the accuracy of surgical planning. The goal of this study is to apply machine leaning techniques to describing pre-operative and post-operative vena caval flow conditions in Fontan patients in order to develop predictions of post-operative boundary conditions to be used in surgical planning. Based on a virtual cohort synthesized by lumped-parameter models, we proposed a novel diversity-aware generative adversarial active learning framework to successfully train predictive deep neural networks on very limited amount of cases that are generally faced by cardiovascular studies. Results of 14 groups of experiments uniquely combining different data query strategies, metrics, and data augmentation options with generative adversarial networks demonstrated that the highest overall prediction accuracy and coefficient of determination were exhibited by the proposed method. This framework serves as a first step toward deep learning for cardiovascular flow prediction/regression with reduced labeling requirements and augmented learning space.