  In this pilot study, we investigate the use of a deep learning (DL) model to
temporally evolve the dynamics of gas accreting onto a black hole in the form
of a radiatively inefficient accretion flow (RIAF). We have trained a machine
to forecast such a spatiotemporally chaotic system -- i.e. black hole weather
forecasting -- using a convolutional neural network (CNN) and a training
dataset which consists of numerical solutions of the hydrodynamical equations,
for a range of initial conditions. We find that deep neural networks seem to
learn well black hole accretion physics and evolve the accretion flow orders of
magnitude faster than traditional numerical solvers, while maintaining a
reasonable accuracy for a long time. For instance, CNNs predict well the
temporal evolution of a RIAF over a long duration of $8\times 10^4 GM/c^3$,
which corresponds to 80 dynamical times at $r=100 GM/c^2$. The DL model is able
to evolve flows from initial conditions not present in the training dataset
with good accuracy. Our approach thus seems to generalize well. Once trained,
the DL model evolves a turbulent RIAF on a single GPU four orders of magnitude
faster than usual fluid dynamics integrators running in parallel on 200 CPU
cores. We speculate that a data-driven machine learning approach should be very
promising for accelerating not only fluid dynamics simulations, but also
general relativistic magnetohydrodynamic ones.
