We present a novel approach for hybrid performance modelling and prediction of large-scale parallel and distributed computing systems, which combines Mathematical Modelling (MathMod) and Discrete-Event Simulation (DES). We use MathMod to develop parameterised performance models for components of the system. Thereafter, we use DES to describe the structure of system and the interaction among its components. As a result we obtain a high-level performance model, which combines the evaluation speed of mathematical models with the structure awareness and fidelity of the simulation model. We evaluate empirically our approach with a real-world material science program that comprises more than 15,000 lines of code.