Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-Set Method. (arXiv:2201.12342v3 [math.NA] UPDATED)

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 …

arxiv computation error math networks neural networks set