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It is tested whether machine learning methods can be used for preconditioningto increase the performance of the linear solver -- the backbone of thesemi-implicit, grid-point model approach for weather and climate models.Embedding the machine-learning method within the framework of a linear solvercircumvents potential robustness issues that machine learning approaches areoften criticized for, as the linear solver ensures that a sufficient, pre-setlevel of accuracy is reached. The approach does not require prior availabilityof a conventional preconditioner and is highly flexible regarding complexityand machine learning design choices. Several machine learning methods are usedto learn the optimal preconditioner for a shallow-water model withsemi-implicit timestepping that is conceptually similar to more complexatmosphere models. The machine-learning preconditioner is competitive with aconventional preconditioner and provides good results even if it is usedoutside of the dynamical range of the training dataset.

Machine-Learned Preconditioners for Linear Solvers in Geophysical Fluid Flows