We describe and evaluate a physics-based proxy model approach for reservoir prediction and optimization. It builds on the recent development of so-called flow-network models which represent flow paths between wells by discrete 1D grids with permeability and pore volume properties. These types of models represent an alternative to capacitance resistance and correlation-based models and have the benefit of allowing for all physics supported by regular 3D grid-based commercial simulators. The new model is different from a previously proposed model in that we include additional nodes in the network that allow for more and indirect flow paths between wells, as well as extra nodes to represent an aquifer. We describe the structure of our flow network and investigate the impact of design and training parameters on the performance of the network, both in history matching and prediction mode. Examples include the number and placement of network nodes, the treatment of aquifers, and the size and sampling of prior model property values. We distinguish between the accuracy of the history match and the generalizability by cross-validating the flow network performance on future well control strategies that are different from that encountered during the history period. Using this procedure, we aim to prevent overfitting of the model while ensuring sufficient predictive power. Results are presented for experiments based on phase rate and bottom hole pressure measurements and predictions generated with the Brugge benchmark model which is used as a synthetic truth. We subsequently present a first application of flow network models for well control optimization under uncertainty. To this end we employ a stochastic simplex gradient-based optimization approach and demonstrate that strategies that are expected to deliver improved NPV can be identified at much lower computational cost and within a much shorter time frame than would be required otherwise.