Network tomography is a discipline that aims to infer the internal network characteristics from end-to-end correlated measurements performed at the network edge. This work presents a new tomography approach for link metrics inference in an SDN/NFV environment (even if it can be exported outside this field) that we called TOM (Tomography for Overlay networks Monitoring). In such an environment, we are particularly interested in supervising network slicing, a recent tool enabling to create multiple virtual networks for different applications and QoS constraints on a Telco infrastructure. The goal is to infer the underlay resources states from the measurements performed in the overlay structure. We model the inference task as a regression problem that we solve following a Neural Network approach. Since getting labeled data for the training phase can be costly, our procedure generates artificial data for the training phase. By creating a large set of random training examples, the Neural Network learns the relations between the measures done at path and link levels. This approach takes advantage of efficient Machine Learning solutions to solve a classic inference problem. Simulations with a public dataset show very promising results compared to statistical-based methods. We explored mainly additive metrics such as delays or logs of loss rates, but the approach can also be used for non-additive ones such as bandwidth.