A Hybrid Inference System for Improved Curvature Estimation in the Level-Set Method Using Machine Learning

This is the accompanying repository for our hybrid inference system that approximates mean curvature in the level-set method. The neural networks here available were trained on the negative curvature spectrum, with samples from two-dimensional circular and sinusoidal interfaces. We considered 4 different mesh sizes: 2^{-7}, 2^{-8}, 2^{-9}, and 2^{-10}. We have grouped the corresponding models into 4 folders: 7, 8, 9, and 10. These numbers also represent the maximum levels of refinement of the quadtrees we used in our C++ parallel level-set library.

You'll find in each folder:

• The trained model (in *.h5 format),
• The pickled transformer object (PCA) for data preprocessing,
• Some stats, and
• Two plots comparing the numerical (scatterNumerics.png) and the neural (scatterReinit.png) approximations to mean curvature for (train + test + validation) samples obtained with level-set (10-iteration, PDE) reinitialization.

Feel free to forward your questions to this email.