  Research within the field of multiscale modelling seeks, amongst other
questions, to reconcile atomistic scale interactions with thermodynamical
quantities (such as stress) on the continuum scale. The estimation of stress at
a continuum point on the atomistic scale requires a pre-defined kernel
function. This kernel function derives the stress at a continuum point by
averaging the contribution from atoms within a region surrounding the continuum
point. Commonly the kernel weight assignment is isotropic: an identical weight
is assigned to atoms at the same spatial distance, which is tantamount to a
local constant regression model. In this paper we employ a local linear
regression model and leverage the mechanism of automatic kernel carpentry to
allow for spatial averaging adaptive to the local distribution of atoms. As a
result, different weights may be assigned to atoms at the same spatial
distance. This is of interest for determining atomistic stress at stacking
faults, interfaces or surfaces. It is shown in this study that for crystalline
solids, although the local linear regression model performs elegantly, the
additional computational costs are not justified compared to the local constant
regression model.
