Current progress in sensor technology is setting the stage to move closer to satisfactory solutions to challenging engineering problems, like e.g. system identification and structural health monitoring (SHM). In civil engineering, SHM is often based on the analysis of vibrational recordings, represented by time histories of displacements and/or accelerations collected through pervasive sensor networks and shaped as Multivariate Time Series (MTS). Despite the great advances in soft computing techniques like neural networks, inverse problems featuring regression tasks on the raw vibrational measurements are still challenging. Developing dimensionality reduction tools, able to infer complex correlations within and across the recorded time series, stands as a must. In this work, we have designed an AutoEncoder (AE) capable of condensing MTS-shaped data in a vector featuring a few latent variables only. The obtained reduced data representation allows the solution of inverse problems, like e.g. the identification of the parameters governing the dynamic load applied to a structural system. Inception modules and residual learning are respectively exploited for the encoding and the decoding parts of the AE, enhancing the informative content of the latent variables. Numerical examples, aimed at the identification of the loading conditions on a shear-type building, are reported to assess the effectiveness of the proposed procedure.