Traditionally, modeling of single-screw extrusion is often limited to predicting the throughput-pressure behavior by considering the flow in the screw channels. Aside from the throughput-pressure relationship, viscous dissipation, power demand, and temperature development are of major importance and can be predicted by various melt-conveying models that fall into two categories: (i) closed-form analytical models that are based on Newtonian flow-theory and (ii) approximation and regression models that are based on non-Newtonian flow-theory. These approaches, generally, ignore leakage flow, the effect of which in conventional screw designs, is moderate on the throughput-pressure relationship, but significant on power demand. In this work, we present a novel modeling approach that accurately incorporates leakage flow into the prediction of power demand and viscous dissipation. First, novel leakage models for the viscous dissipation rate of the flow between screw flights and barrel surface were developed. To this end, a parametrically driven design study was carried out. The viscous dissipation rate was evaluated based on the flow field in the flight gap solved numerically for approximately 9,230 independent design points. This data set served as input for generating a symbolic regression model by means of genetic algorithms. Second, we implemented these novel, highly accurate models in a network-theory-based screw simulation routine consisting of two overlaid networks: one that predicts throughput-pressure and another that predicts temperature and power demand. In this context, the leakage viscous dissipation models were applied to determine the local dissipation rate in the gap between flights and barrel, which was then used to predict power demand and temperature development. Finally, we evaluated our model by simulating various screw designs with different processing conditions and polymeric materials.