  In this study, we employ eth-operators and spin-weighted spherical harmonics
to express the ADM mass of a static space-time based on the mean values of its
components over a a radius-$r$ sphere. While initially derived for standard
spherical coordinates, we showcase its adaptability by demonstrating its
usefulness in expressing a quasilocal mass; specifically, the Bartnik mass, of
an almost round 2D-hypersurface in terms of some specific boundary conditions.
Additionally, we utilize this formulation to propose a deep learning
methodology for numerically constructing static metrics that incorporate
2D-hypersurfaces with specified Bartnik mass.
