  Fourier neural operators (FNOs) are a recently introduced neural network
architecture for learning solution operators of partial differential equations
(PDEs), which have been shown to perform significantly better than comparable
deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple
orders of magnitude over conventional numerical PDE solvers. However, due to
the high dimensionality of their input data and network weights, FNOs have so
far only been applied to two-dimensional or small three-dimensional problems.
To remove this limited problem-size barrier, we propose a model-parallel
version of FNOs based on domain-decomposition of both the input data and
network weights. We demonstrate that our model-parallel FNO is able to predict
time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up
to 512 A100 GPUs and show an example of training a distributed FNO on the Azure
cloud for simulating multiphase CO$_2$ dynamics in the Earth's subsurface.
