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The quality of a steel arc-welded joint greatly depends on the parameters of the welding process used. Given a particular geometry of the weld, the corresponding welding materials and the restraints used to fix the parts, the feed rate, the speed and the heat input play a significant role in the thermal and elasto-plastic response of the plates. Residual stresses and overall distortions are always of great concern in welding processes and a number of simulation approaches have been developed to assess this behavior. However, these simulations are very computationally intense, making it extremely costly to optimize weld designs. In the paper, a strategically selected set of finite element simulations of a typical welding process are made to train a neural network model, which in turn can be used to effectively predict the weld response at a minimal fraction of the effort required by a standard finite element simulation.