Current progress in sensor technology is setting the ground to push toward 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 such as neural networks, inverse problems featuring regression tasks on raw vibrational measurements are still challenging. Developing dimensionality reduction tools, able to infer complex correlations within and across the recorded time series, is then of paramount importance. In this work, we designed an AutoEncoder (AE) capable of condensing MTS-shaped data in a reduced format featuring a few latent variables only. The obtained reduced data representation enhances the solution of inverse problems, like e.g., the identification of the parameters governing the dynamic load applied to a structural system. 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.