  We developed and applied a machine-learned discretization for one-dimensional
(1-D) horizontal passive scalar advection, which is an operator component
common to all chemical transport models (CTMs). Our learned advection scheme
resembles a second-order accuracy, three-stencil numerical solver, but differs
from a traditional solver in that coefficients for each equation term are
output by a neural network rather than being theoretically-derived constants.
We downsampled higher-resolution simulation results -- resulting in up to
16$\times$ larger grid size and 64$\times$ larger timestep -- and trained our
neural network-based scheme to match the downsampled integration data. In this
way, we created an operator that is low-resolution (in time or space) but can
reproduce the behavior of a high-resolution traditional solver. Our model shows
high fidelity in reproducing its training dataset (a single 10-day 1-D
simulation) and is similarly accurate in simulations with unseen initial
conditions, wind fields, and grid spacing. In many cases, our learned solver is
more accurate than a low-resolution version of the reference solver, but the
low-resolution reference solver achieves greater computational speedup
(500$\times$ acceleration) over the high-resolution simulation than the learned
solver is able to (18$\times$ acceleration). Surprisingly, our learned 1-D
scheme -- when combined with a splitting technique -- can be used to predict
2-D advection, and is in some cases more stable and accurate than the
low-resolution reference solver in 2-D. Overall, our results suggest that
learned advection operators may offer a higher-accuracy method for accelerating
CTM simulations as compared to simply running a traditional integrator at low
resolution.
