Coarsening in algebraic multigrid using Gaussian processes

Multigrid methods have proven to be an invaluable tool efficiently solve large sparse linear systems arising in the discretization of Partial Differential Equations (PDEs). Algebraic multigrid and particular adaptive algebraic approaches shown that efficiency can obtained without having resort properties PDE. Yet required setup these poses a not negligible overhead cost. Methods from machine learning attracted attention streamline processes based on statistical models being trained available data. Interpreting algebraically smooth error as instance Gaussian process, we develop new, data driven approach construct methods. Based priori distributions, kriging interpolation minimizes mean squared posteriori distribution, given coarse grid. Going one step further, exploit quantification uncertainty process model order efficient variable splittings. Using semivariogram fit suitable covariance demonstrate our yields using single vector.