  We propose the use of physics-informed neural networks for solving the
shallow-water equations on the sphere in the meteorological context.
Physics-informed neural networks are trained to satisfy the differential
equations along with the prescribed initial and boundary data, and thus can be
seen as an alternative approach to solving differential equations compared to
traditional numerical approaches such as finite difference, finite volume or
spectral methods. We discuss the training difficulties of physics-informed
neural networks for the shallow-water equations on the sphere and propose a
simple multi-model approach to tackle test cases of comparatively long time
intervals. Here we train a sequence of neural networks instead of a single
neural network for the entire integration interval. We also avoid the use of a
boundary value loss by encoding the boundary conditions in a custom neural
network layer. We illustrate the abilities of the method by solving the most
prominent test cases proposed by Williamson et al. [J. Comput. Phys. 102
(1992), 211-224].
