Key Points: • A U-Net is refined to forecast seven atmospheric variables on global scale, falling behind the state-of-the-art by only one day. • Forecasts are generated on the HEALPix mesh, facilitating the development of location invariant convolution kernels. • Without converging to climatology, the model produces stable and realistic states 13 of the atmosphere in 365-days rollouts. Abstract: We present a parsimonious deep learning weather prediction model on the Hierarchical Equal Area isoLatitude Pixelization (HEALPix) to forecast seven atmospheric variables for arbitrarily long lead times on a global approximately 110 km mesh at 3h time resolution. In comparison to state-of-the-art machine learning weather forecast models, such as Pangu-Weather and GraphCast, our DLWP-HPX model uses coarser resolution and far fewer prognostic variables. Yet, at one-week lead times its skill is only about one day behind the state-of-the-art numerical weather prediction model from the European Centre for Medium-Range Weather Forecasts. We report successive forecast improvements resulting from model design and data-related decisions, such as switching from the cubed sphere to the HEALPix mesh, inverting the channel depth of the U-Net, and introducing gated recurrent units (GRU) on each level of the U-Net hierarchy. The consistent east-west orientation of all cells on the HEALPix mesh facilitates the development of location-invariant convolution kernels that are successfully applied to propagate global weather patterns across our planet. Without any loss of spectral power after two days, the model can be unrolled autoregressively for hundreds of steps into the future to generate stable and realistic states of the atmosphere that respect seasonal trends, as showcased in one year simulations. Our parsimonious DLWP-HPX model is research-friendly and potentially well-suited for sub-seasonal and seasonal forecasting. Plain Language Summary: Weather forecasting is traditionally realized by numerical weather prediction models that solve physical equations to simulate the progression of the atmosphere. Numerical methods are compute intense and their performance is increasingly challenged by less compute demanding and highly sophisticated machine learning approaches. Yet, a downside of these new models is their reliability: They are not guaranteed to generate physically plausible states, which often prevents them from generating stable and realistic forecasts beyond two weeks into the future. Here, a parsimonious machine learning model is developed to forecast just seven variables of the atmosphere (compared to more than 800 in numerical models and 69 or 218 in competitive machine learning models) over an entire year. Despite the small number of variables, our model generates forecasts that only fall behind expensive state-of-the-art predictions by a single day. That is, our error in a seven-days forecast matches that of a state-of-the-art forecast at day eight. Advancing weather forecasts with research friendly and parsimonious machine learning models beyond two weeks promises to extend horizons for planning in various fields that impact environment, economy, and society.