This is an implementation of the algorithm from:

A. Gruber, M. Gunzburger, L. Ju, Y. Teng, and Z. Wang. Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations,

which learns an intrinsically one-dimensional representation of a (user or data defined) scalar-valued function of many variables.

The main file is "run_algorithm.py", and "options.py" contains the hyperparameters that will be passed when the program is instantiated. These should be modified according to your particular needs.

Alternatively, simply execute "run_algorithm.py" to generate an example of the method.

The code was written and tested using Python 3.8 on Mac OSX 11.2.3. The required dependencies are

• Numpy
• Pytorch
• Matplotlib
• Scipy (for polynomial regression)
• Scikit-learn (for nearest neighbors regression)
• pyDOE (optional: for latin hypercube sampling)

To use your own dataset, you should provide either:

• a scalar-valued function implemented in "functions.py"
• a filepath to an array of length nSamples with feature blocks structured like [domain_variables, function_outputs, gradients]. Take a look at the function preprocess_data implemented in "trainer.py", as well as the files in the data directory for an example.

Please cite our paper if you use this code in your own work:

@article{gruber2021nonlinear,
  title={Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations.},
  author={Gruber, Anthony and Gunzburger, Max and Ju, Lili and Teng, Yuankai and Wang, Zhu},
  journal={Numerical Mathematics: Theory, Methods \& Applications},
  volume={14},
  number={4},
  year={2021}
}