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Network tomography, a classic research problem in the realm of network monitoring, refers to the methodology of inferring unmeasured network attributes using selected end-to-end path measurements. In the research community, network tomography is generally investigated under the assumptions of known network topology, correlated path measurements, bounded number of faulty nodes/links, or even special network protocol support. The applicability of network tomography is considerably constrained by these strong assumptions, which therefore frequently position it in the theoretical world. In this regard, we revisit network tomography from the practical perspective by establishing a generic framework that does not rely on any of these assumptions or the types of performance metrics. Given only the end-to-end path performance metrics of sampled node pairs, the proposed framework, NeuTomography, utilizes deep neural network and data augmentation to predict the unmeasured performance metrics via learning non-linear relationships between node pairs and underlying unknown topological/routing properties. In addition, NeuTomography can be employed to reconstruct the original network topology, which is critical to most network planning tasks. Extensive experiments using real network data show that comparing to baseline solutions, NeuTomography can predict network characteristics and reconstruct network topologies with significantly higher accuracy and robustness using only limited measurement data.