Modeling metal additive manufacturing processes is of great importance because it allows for the production of objects that are closer to the desired geometry and mechanical properties. Over-deposition often takes place during laser metal deposition, especially when the deposition head changes its direction and results in more material being melted onto the substrate. Modeling over-deposition is one of the necessary steps toward online process control, as a good model can be used in a closed-loop system to adjust the deposition parameters in real-time to reduce this phenomenon. In this study, we present a long-short memory neural network to model over-deposition. The model has been trained on simple geometries such as straight tracks, spiral and V-tracks made of Inconel 718. The model shows good generalization capabilities and can predict the height of more complex and previously unseen random tracks with limited performance loss. After the addition to the training dataset of a small amount of data coming from the random tracks, the performance of the model for such additional shapes improves significantly, making this approach feasible for more general applications as well.