Numerical simulators are essential tools in the study of natural
fluid-systems, but their performance often limits application in practice.
Recent machine-learning approaches have demonstrated their ability to
accelerate spatio-temporal predictions, although, with only moderate accuracy
in comparison. Here we introduce MultiScaleGNN, a novel multi-scale graph
neural network model for learning to infer unsteady continuum mechanics in
problems encompassing a range of length scales and complex boundary geometries.
We demonstrate this method on advection problems and incompressible fluid
dynamics, both fundamental phenomena in oceanic and atmospheric processes. Our
results show good extrapolation to new domain geometries and parameters for
long-term temporal simulations. Simulations obtained with MultiScaleGNN are
between two and four orders of magnitude faster than those on which it was
trained.