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The goal of Specular Neutron and X-ray Reflectometry is to infer materials Scattering Length Density (SLD) profiles from experimental reflectivity curves. This paper focuses on investigating an original approach to the ill-posed non-invertible problem which involves the use of Artificial Neural Networks (ANN). In particular, the numerical experiments described here deal with large data sets of simulated reflectivity curves and SLD profiles, and aim to assess the applicability of Data Science and Machine Learning technology to the analysis of data generated at neutron scattering large scale facilities. It is demonstrated that, under certain circumstances, properly trained Deep Neural Networks are capable of correctly recovering plausible SLD profiles when presented with never-seen-before simulated reflectivity curves. When the necessary conditions are met, a proper implementation of the described approach would offer two main advantages over traditional fitting methods when dealing with real experiments, namely, 1. sample physical models are described under a new paradigm: detailed layer-by-layer descriptions (SLDs, thicknesses, roughnesses) are replaced by parameter free curves $ρ(z)$, allowing a-priori assumptions to be fed in terms of the sample family to which a given sample belongs (e.g. "thin film", "lamellar structure", etc.) 2. the time-to-solution is shrunk by orders of magnitude, enabling faster batch analyses for large datasets.