A deep learning approach for the computation of curvature in the level-set method. (arXiv:2002.02804v4 [math.NA] UPDATED)

We propose a deep learning strategy to estimate the mean curvature of
two-dimensional implicit interfaces in the level-set method. Our approach is
based on fitting feed-forward neural networks to synthetic data sets
constructed from circular interfaces immersed in uniform grids of various
resolutions. These multilayer perceptrons process the level-set values from
mesh points next to the free boundary and output the dimensionless curvature at
their closest locations on the interface. Accuracy analyses involving irregular
interfaces, in both uniform and adaptive …

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