We discuss modelling approaches for interacting particle systems with applications ranging from self-propelled systems such as bird flocks to purpose driven systems like pedestrian dynamics. Classical models use potential-based forces to incorporate common observations from real word. With the amount of data available today, we can fit the model parameters or learn neural networks as substitute force models. The fitting or learning problems are framed as optimization tasks which allow for rigorous mathematical analysis and the derivation of first-order optimization algorithms. Theoretical results will be presented as well as numerical simulations and outcomes of the algorithms.