  We present a novel hybrid strategy based on machine learning to improve
curvature estimation in the level-set method. The proposed inference system
couples enhanced neural networks with standard numerical schemes to compute
curvature more accurately. The core of our hybrid framework is a switching
mechanism that relies on well established numerical techniques to gauge
curvature. If the curvature magnitude is larger than a resolution-dependent
threshold, it uses a neural network to yield a better approximation. Our
networks are multilayer perceptrons fitted to synthetic data sets composed of
sinusoidal- and circular-interface samples at various configurations. To reduce
data set size and training complexity, we leverage the problem's characteristic
symmetry and build our models on just half of the curvature spectrum. These
savings lead to a powerful inference system able to outperform any of its
numerical or neural component alone. Experiments with stationary, smooth
interfaces show that our hybrid solver is notably superior to conventional
numerical methods in coarse grids and along steep interface regions. Compared
to prior research, we have observed outstanding gains in precision after
training the regression model with data pairs from more than a single interface
type and transforming data with specialized input preprocessing. In particular,
our findings confirm that machine learning is a promising venue for reducing or
removing mass loss in the level-set method.
