  In spite of considerable progress, computing curvature in Volume of Fluid
(VOF) methods continues to be a challenge. The goal is to develop a function or
a subroutine that returns the curvature in computational cells containing an
interface separating two immiscible fluids, given the volume fraction in the
cell and the adjacent cells. Currently, the most accurate approach is to fit a
curve (2D), or a surface (3D), matching the volume fractions and finding the
curvature by differentiation. Here, a different approach is examined. A
synthetic data set, relating curvature to volume fractions, is generated using
well-defined shapes where the curvature and volume fractions are easily found
and then machine learning is used to fit the data (training). The resulting
function is used to find the curvature for shapes not used for the training and
implemented into a code to track moving interfaces. The results suggest that
using machine learning to generate the relationship is a viable approach that
results in reasonably accurate predictions.
