The inversion problem dealt with is identification of the parameters of a magma-filled dike, which causes observable changes in various geophysical fields, using Artificial Neural Networks (ANNs). The inversion approach, which is based on the function approximation capabilities of Multi-layer Perceptrons (MLPs), is also carried out by a systematic search technique based on the Simulated Annealing (SA) optimization algorithm, in order to emphasize the peculiarities of the proposed strategy. In the paper, it is demonstrated that MLPs, once correctly trained, can solve the inversion problem very fast with an appreciable degree of accuracy. It also demonstrated that an integrated approach involving geophysical data of different types, allows for a more accurate solution than when only ground deformation data is considered.