  We present an error-neural-modeling-based strategy for approximating
two-dimensional curvature in the level-set method. Our main contribution is a
redesigned hybrid solver [Larios-C\'ardenas and Gibou, J. Comput. Phys. (May
2022), 10.1016/j.jcp.2022.111291] that relies on numerical schemes to enable
machine-learning operations on demand. In particular, our routine features
double predicting to harness curvature symmetry invariance in favor of
precision and stability. The core of this solver is a multilayer perceptron
trained on circular- and sinusoidal-interface samples. Its role is to quantify
the error in numerical curvature approximations and emit corrected estimates
for select grid vertices along the free boundary. These corrections arise in
response to preprocessed context level-set, curvature, and gradient data. To
promote neural capacity, we have adopted sample negative-curvature
normalization, reorientation, and reflection-based augmentation. In the same
manner, our system incorporates dimensionality reduction, well-balancedness,
and regularization to minimize outlying effects. Our training approach is
likewise scalable across mesh sizes. For this purpose, we have introduced
dimensionless parametrization and probabilistic subsampling during data
production. Together, all these elements have improved the accuracy and
efficiency of curvature calculations around under-resolved regions. In most
experiments, our strategy has outperformed the numerical baseline at twice the
number of redistancing steps while requiring only a fraction of the cost.
