When attempting to make global weather predictions with machine learning methods, one needs to map high-dimensional input (3 or 4D-atmospheric fields) to high dimensional output (3 or 4D-atmospheric fields). We know that due to the chaoticity of the atmosphere this mapping is highly non-linear, which makes the problem difficult but also very interesting to work on. An additional challenge is the large size of the involved data. I will present some progress we have on this using convolutional neuronal networks, and mainly discuss general problems/design-choices/issues with this type of machine-learning problems.