Nanostructured metamaterials are now commonplace in contemporary photonics, providing a means for tailored manipulation of light-matter interactions. By deliberately altering the spatial distribution of materials at sub-wavelength scales, these materials yield optical responses surpassing those seen in natural counterparts. Among these, thin-film metamaterials, characterized by varied material compositions along a single axis, have captured significant attention. Widely employed in applications like optical coatings and sensors, they exemplify the versatility and impact of metamaterial technology. However, the inverse design (ID) of metamaterials, which is crucial for a large set of nanophotonic applications, often encounters challenges due to the vast parameter space inherent in multilayered systems. Starting from conventional methods relying on convolutional neural networks (CNNs), we propose a novel approach employing a LSTM-based architecture that leverages ellipsometric spectra to predict the thickness and material of a N-layered structure. We conduct a comparative analysis revealing a greater effectiveness of our LSTM-based approach, particularly when the number of layers increases. Indeed, our model is able to capture a deeper relationship between the optical features extracted from the ellipsometric spectra and the metamaterials structures.