The “Astrophysical Simualtions of Gravitational-Wave Sources” work package focuses on developing state-of-the-art, machine-learning-enhanced, astrophysical and cosmological simulations of gravitational-wave source populations across all scales, from binary white-dwarves to binary supermassive black holes, and from the Milky Way to the distant universe and the cosmic dawn. Actual data from Einstein Telescope and LISA is at least another decade away. However, we need to be ready to analyze them and be confident about what we can learn well before that. The predictions of these simulations are used to construct realistic synthetic data that benchmark the data analysis methods and the overall capabilities of the observatories, including the rates and property distributions of the expected observed gravitational-wave sources. Inversely, the same simulations are necessary for population inference studies that will tell us which unknown or poorly understood physics can be constrained from ET and LISA observations. In order to overcome the computational cost barriers and achieve the physical realism envisioned for this flagship suite of astrophysical gravitational source simulations, a series of machine learning emulators will be employed for normally unresolved, complex physical processes and to explore the large parameter space of the unavoidable model parameter.