The production of parts by pressing and subsequent welding is commonly used in the automotive industry. The disadvantage of this method of production is that inaccuracies arising during pressing significantly affect the final dimension of the part. However, this can be corrected by the choice of the technological parameters of the following operation—welding. Suitably designed parameters make it possible to partially eliminate inaccuracies arising during pressing and thus increase the overall applicability of this technology. The paper is focused on the upper arm geometry of a car produced in this manner. There have been two neural networks proposed in which the optimal welding parameters are determined based on the stamped dimensions and the desired final dimensions. The Levenberg–Marquardt back-propagation algorithm and the Bayesian regularised back-propagation algorithm were used as the learning algorithm for ANNs in multi-layer feed-forward networks. The outputs obtained from the neural networks were compared with a linear prediction model based on a on the design of experiment methodology. The mean absolute percentage error of the linear regression model on the entire dataset was 3 × 10−3%. A neural network with Levenberg–Marquardt back-propagation learning algorithm had a mean absolute percentage error of 4 × 10−3. Similarly, a neural network with a Bayesian regularised back-propagation learning algorithm had a mean absolute percentage error of 3 × 10−3%.