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Electron beam butt welding of stainless steel (SS 304) and electrolytically tough pitched (ETP) copper plates was carried out according to central composite design of experiments. Three input parameters, namely accelerating voltage, beam current and weld speed were considered in the butt welding experiments of dissimilar metals. The weld-bead parameters, such as bead width and depth of penetration, and weld strength in terms of yield strength and ultimate tensile strength were measured as the responses of the process. Input-output relationships were established in the forward direction using regression analysis, back-propagation neural network (BPNN), genetic algorithm-tuned neural network (GANN) and particle swarm optimization algorithm-tuned neural network (PSONN). Reverse mapping of this process was also conducted using the BPNN, GANN and PSONN approaches, although the same could not be done from the obtained regression equations. Neural networks were found to tackle the problems of both forward and reverse mappings efficiently. However, neural networks tuned by the genetic algorithm and particle swarm optimization algorithm were seen to perform better than the BPNN in most of the cases but not all.