  We present a hybrid strategy based on deep learning to compute mean curvature
in the level-set method. The proposed inference system combines a dictionary of
improved regression models with standard numerical schemes to estimate
curvature more accurately. The core of our 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 multi-layer
perceptrons fitted to synthetic data sets composed of circular- and
sinusoidal-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 result
in compact networks able to outperform any of the system's numerical or neural
component alone. Experiments with static interfaces show that our hybrid
approach is suitable and notoriously superior to conventional numerical methods
in under-resolved and steep, concave regions. Compared to prior research, we
have observed outstanding gains in precision after including training data
pairs from more than a single interface type and other means of input
preprocessing. In particular, our findings confirm that machine learning is a
promising venue for devising viable solutions to the level-set method's
numerical shortcomings.
