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Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) incompleteness of physics-based models and (2) limited representativeness of the training dataset for data-driven models. Combining the advantages of these two directions while overcoming some of their limitations, we propose a novel hybrid framework for fusing the information from physics-based performance models with deep learning algorithms for prognostics of complex safety-critical systems under real-world scenarios. In the proposed framework, we use physics-based performance models to infer unobservable model parameters related to a system's components health solving a calibration problem. These parameters are subsequently combined with sensor readings and used as input to a deep neural network to generate a data-driven prognostics model with physics-augmented features. The performance of the hybrid framework is evaluated on an extensive case study comprising run-to-failure degradation trajectories from a fleet of nine turbofan engines under real flight conditions. The experimental results show that the hybrid framework outperforms purely data-driven approaches by extending the prediction horizon by nearly 127\%. Furthermore, it requires less training data and is less sensitive to the limited representativeness of the dataset compared to purely data-driven approaches.