“…or hydrology [6]. The majority of ML-based parametrizations, however, is local [48,94,17,18,19,141,26,6,54,79,105,78,99,136,110], i.e., the in-and output are variables of single grid points, which assumes perfect scale separation, for example, in isotropic homogeneous turbulent flows [96]. However, local parametrizations are inaccurate; for example in the case of anisotropic nonhomogeneous dynamics [96,129], for correcting global error for coarse spectral discretizations [15], or in large-scale climate models [40,100].…”