Software is pervasive and often critical in our everyday life. Its production is complicated and expensive, especially for complex systems like Cyber-Physical Systems (CPS). CPS are often safety-critical and rely on heterogeneous processors (e.g. CPUs, GPUs, FPGAs, DSPs), hence their engineering requires reliable and flexible methods. Domain-Specific Modelling Languages (DSML) and model-based techniques have proven to be very suitable for that. Currently, from DSMLs, executables are generated by first translating a model to a program in a high-level programming language (e.g. C++) via code generators and then compile it. Code generators are language-specific, inflexible, and not always reliable, difficult and expensive to certify, customise and maintain. The purpose of ORPHEUS is to study and formalise a systematic and precise theory for model compilation, implement it in a prototypical framework, and evaluate it through mixed-method studies on an industrial case-study. This kind of solution will maximise the profit of using model-based techniques, thus producing high-quality and safe software in a more efficient manner, and accelerate research by providing a unified common ground for researchers and practitioners. The project is run through 4-steps cycles of 1) theoretical solution, 2) formalisation, 3) prototyping, and 4) evaluation. The research is carried out by the PI, two professors with expertise in complementary areas, a postdoc and a Ph.D. student.