Physics-Assisted and Topology-Informed Deep Learning for Weather
  Prediction
Authors: name: Jiaqi Zheng, name: Qing Ling, name: Yerong Feng

Although deep learning models have demonstrated remarkable potential in
weather prediction, most of them overlook either the physics of the
underlying weather evolution or the topology of the Earth's surface.
In light of these disadvantages, we develop PASSAT, a novel Physics-ASSisted
And Topology-informed deep learning model for weather prediction. PASSAT
attributes the weather evolution to two key factors: (i) the advection process
that can be characterized by the advection equation and the Navier-Stokes
equation; (ii) the Earth-atmosphere interaction that is difficult to both model
and calculate. PASSAT also takes the topology of the Earth's surface into
consideration, other than simply treating it as a plane. With these
considerations, PASSAT numerically solves the advection equation and the
Navier-Stokes equation on the spherical manifold, utilizes a spherical graph
neural network to capture the Earth-atmosphere interaction, and generates the
initial velocity fields that are critical to solving the advection equation
from the same spherical graph neural network. In the 5.625^circ-resolution
ERA5 data set, PASSAT outperforms both the state-of-the-art deep learning-based
weather prediction models and the operational numerical weather prediction
model IFS T42. Code and checkpoint are available at
https://github.com/Yumenomae/PASSAT_5p625.