The accurate prediction of the curvature of fluid-fluid interfaces is crucial for appropriately modeling the surface forces when computing two-phase flows with immiscible fluids. The volume of fluid (VOF) method is often used for these computations to specify the different fluids and the interface by the so-called volume fraction field. In this study, a deep artificial neural network is trained to predict the interface curvature from the volume fraction values. This approach is investigated within an algebraic VOF framework. A rudimentary interface resharpening algorithm is introduced for the input stencils to enhance the accuracy and robustness when the interface can not be captured entirely sharp. The performance of different neural network architectures is evaluated by generic test data and the computation of two oscillating droplet flow configurations.