Despite steady improvements in numerical weather prediction models, they still exhibit systematic errors caused by simplified representations of physical processes, assumptions about linear behavior, and the challenges of integrating all available observational data. Weather services around the world now recognize that addressing these shortcomings through the use of artificial intelligence (AI) could revolutionize the discipline in the coming decades. This will require a fundamental shift in thinking that integrates meteorology much more closely with mathematics and computer science. TEEMLEAP will foster this cultural change through a collaboration of scientists from the KIT Climate and Environment and MathSEE centers by establishing an idealized testbed to explore machine learning in weather forecasting. In contrast to weather services, which naturally focus on improvements of numerical forecast models in their full complexity, TEEMLEAP intends to evaluate the application possibilities and benefits of AI in this testbed along the entire process chain of weather forecasting.