At present, District Heating Networks (DHNs) are required to operate more and more reliably and efficiently in order to further save primary energy and reduce environmental impact. Thus, monitoring and diagnostic approaches are necessary to identify the typical faults that affect this type of systems (e.g., anomalous heat and pressure losses), with the final goal of optimizing DHN operation and management. To this aim, this paper presents a data-driven diagnostic methodology that exploits NARX (nonlinear autoregressive network with exogenous inputs) neural networks to simulate DHN healthy operation and a threshold-based criterion for fault detection and identification. The novel diagnostic methodology is tested for evaluating the health state of the DHN of the campus of the University of Parma (Italy), based on the availability of time series of measurable variables (mass flow rate, pressure, and temperature) for both the power plant and the end-users. Both single and multiple faults of anomalous heat losses and anomalous pressure losses, with different magnitudes and location, were artificially implanted in DHN pipes. The main novel contribution of this paper with respect to state-of-the-art literature relies on the development of a real-time simulation approach aimed to predict DHN future operation and detect abnormal deviations from normal operation. The methodology proves to correctly detect and identify all simulated faults related to heat and pressure losses, by also correctly estimating their magnitude even in the most challenging scenarios.