What can a machine learn about weather?

Computing weather is a complex, coupled multi-scale problem with almost infinite degrees of freedom. Numerical weather prediction models running on high-end HPC systems use a combination of numerical solvers for differential equations and empirical parametrisations to forecast weather at spatial resolution of around 10 km for up to 10 days. Recently, the weather and climate community has begun to explore many different ways in which machine learning could help improve weather forecasting or make it computationally less demanding and therefore more energy efficient. While some approaches are very successful others aren't and this leads to the question of fundamental data properties that must be "understood" by a machine to make a skillful prediction and estimate the uncertainty of that prediction. What aspects of ML models do we need to focus on to achieve better results? And can we assume that larger deep learning models perform better?