Due to the rising demand for individualized product specifications and short innovation cycles, industrial robots gain increasing attention for machining operations as milling and forming. Limitations in their absolute positional accuracy are addressed by enhanced modelling and calibration techniques. However, the resulting absolute positional accuracy stays in a range still not feasible for general purpose milling and forming tolerances. Improvements of the model accuracy demand complex, often not accessible system knowledge on the expense of realtime capability. This article presents a new approach using artificial neural networks to enhance positional accuracy of industrial robots. A hyperparameter optimization is applied, to overcome the downside of choosing an appropriate artificial neural network structure and training strategy in a trial and error procedure. The effectiveness of the method is validated with a heavy-duty industrial robot. It is demonstrated that artificial neural networks with suitable hyperparameters outperform a kinematic model with calibrated geometric parameters.