  It is tested whether machine learning methods can be used for preconditioning
to increase the performance of the linear solver -- the backbone of the
semi-implicit, grid-point model approach for weather and climate models.
Embedding the machine-learning method within the framework of a linear solver
circumvents potential robustness issues that machine learning approaches are
often criticized for, as the linear solver ensures that a sufficient, pre-set
level of accuracy is reached. The approach does not require prior availability
of a conventional preconditioner and is highly flexible regarding complexity
and machine learning design choices. Several machine learning methods are used
to learn the optimal preconditioner for a shallow-water model with
semi-implicit timestepping that is conceptually similar to more complex
atmosphere models. The machine-learning preconditioner is competitive with a
conventional preconditioner and provides good results even if it is used
outside of the dynamical range of the training dataset.
