Network Slicing (NS) is a key technology that enables network operators to accommodate different types of services with varying needs on a single physical infrastructure. Despite the advantages it brings, NS raises some technical challenges, mainly ensuring the Service Level Agreements (SLA) for each slice. Hence, monitoring the state of these slices will be a priority for ISPs. However, due to the high measurements overhead, it is generally forbidden to directly measure the performance of all of these slices. To overcome this limitation, network tomography is a promising solution, consisting of a set of methods of inferring unmeasured network metrics using end-to-end measurements between monitors. In this work, we focus on inferring the additive metrics of slices such as delays or logarithms of loss rates. We model the inference task as a regression problem that we solve using neural networks. In our approach, we train the model on an artificial dataset. This not only avoids the costly process of collecting a large set of labeled data but has also a nice covering property useful for the procedure's accuracy. Moreover, to handle a change on the topology or the slices we monitor, we propose a solution based on transfer learning in order to find a trade-off between the quality of the solution and the cost to get it. Simulation results with both, emulated and simulated traffic show the efficiency of our method compared to existing ones in terms of both accuracy and computation time.