Injection molding is a popular production process for short fiber reinforced components. The mechanical properties of such components depend on process-induced fiber orientations which are commonly predicted via numerical simulations. However, high computational costs prevent process simulations from being used in iterative procedures, such as topology optimization or finding optimal injection locations. We propose a fast approximation method that extracts nodal features and train a regression model to predict fill states, cooling times, volumetric shrinkage, and fiber orientations. The features are determined by solving eikonal equations with a fast iterative method and computing spatial moments to characterize node-adjacent material distributions. Subsequently, we use these features to train feed forward neural networks and gradient boosted regression trees with simulation data of a large dataset of geometries. This approach is significantly faster than conventional methods, providing 20x speed-up for single simulations and more than 200x speed-up in gate location optimization. It generalizes to arbitrary geometries and injection locations.