README.md

Error-correcting neural networks for three-dimensional mean-curvature computation in the level-set method

By Luis Ángel Larios-Cárdenas and Frédéric Gibou, Computer Science and Mechanical Engineering Departments, University of California, Santa Barabara

Tuesday, August 9, 2022

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This is the accompanying repository for our paper "Machine learning algorithms for three-dimensional mean-curvature computation in the level-set method".
You may also check out the preceding paper and its GitHub repository for the two-dimensional case.

Contents

To prepare the environment, take a look at the requirements.txt file. The neural networks trained for each resolution are organized under the models/η/# folder, where $\eta$ represents the maximum level of refinement of the unit-cube octrees, and # is either non-saddle or saddle. Furthermore, $\eta = 6, 7, ..., 11$, and $h = 1/(2^\eta)$ is the mesh size. The shared files include:

1. k_nnet.h5: TensorFlow/Keras model in HDF5 format (with detached optimizer).
2. k_nnet.json: Our custom JSON version of the neural network with hidden-layer weights encoded in Base64 but decoded as ASCII text. The "output" key refers to the last hidden layer. It does not include the aditive neuron.
3. k_pca_scaler.pkl: PCA scaler stored in pickle format.
4. k_pca_scaler.json: JSON version of PCA scaler with plain-valued parameters.
5. k_std_scaler.pkl: Standard scaler in pickle format.
6. k_std_scaler.json: JSON version of standard scaler with plain-valued parameters.

Testing data sets

We have included sample surface data under the data/ folder for the grid resolution with $\eta = 6$. Each interface has its own subdirectory with different experiment IDs. You can test any of the trained neural networks on this data. See the python/evaluating.py script. To try different experiments, see the multiline strings prefixed with TODO:. You will collect the results from executing python/evaluating.py in the results/ directory

Note: these data sets include 6 samples per interface node. For non-saddle samples, we have already applied negative-mean-curvature normalization but left their curvature data (i.e., hk ($h\kappa^\ast$), ihk ($h\kappa$), h2kg ($h^2\kappa_G^\ast$), and ih2kg ($h^2\kappa_G$)) with the sign intact so we can recover the right answer after computing $h\kappa_\mathcal{F}$. When testing, you might get marginally different results than those reported in our paper. This is because we took the results in the paper from the online inference computations performed in C++, where small floating-point variations are possible.

Contact

Please reach out to Luis Ángel with further questions and/or concerns. We can share the training data sets upon reasonable request as they are quite large. Thanks!