We are interested in numerical simulations where a fundamental task is to solve the Stokes equations in deformable domains. Such domains may contain immiscible fluids separated by interfaces. The project aims to develop numerical methods for efficiently handling systems with many interacting and evolving interfaces. When a large number of interfaces are present, we further aim to develop surrogate models that can provide fast and accurate predictions of the dynamics. These surrogate models will be systematically validated against high-resolution reference simulations. Access to high-performance computing resources is essential in order to generate accurate reference data for training and validation. Therefore, we request computational resources on Dardel.