With the increased availability of condition monitoring data on the one hand and the increased complexity of explicit system physics-based models on the other hand, the application of data-driven approaches for fault detection and isolation has recently grown. While detection accuracy of such approaches is generally very good, their performance on fault isolation often suffers from the fact that fault conditions affect a large portion of the measured signals thereby masking the fault source. To overcome this limitation, we propose a hybrid approach combining physical performance models with deep learning algorithms. Unobserved process variables are inferred with a physics-based performance model to enhance the input space of a data-driven diagnostics model. The resulting increased input space gains representation power enabling more accurate fault detection and isolation. To validate the effectiveness of the proposed method, we generate a condition monitoring dataset of an advanced gas turbine during flight conditions under healthy and four faulty operative conditions based on the Aero-Propulsion System Simulation (C-MAPSS) dynamical model. We evaluate the performance of the proposed hybrid methodology in combination with two different deep learning algorithms: deep feed forward neural networks and Variational Autoencoders, both of which demonstrate a significant improvement when applied within the hybrid fault detection and diagnostics framework. The proposed method is able to outperform pure data-driven solutions, particularly for systems with a high variability of operating conditions. It provides superior results both for fault detection as well as for fault isolation. For the fault isolation task, it overcomes the smearing effect that is commonly observed in pure data-driven approaches and enables a precise isolation of the affected signal. We also demonstrate that deep learning algorithms provide a better performance on the fault detection task compared to the traditional machine learning algorithms.