ChebGreen is a Python library for learning and interpolating Green's function for 1-Dimensional problems in a continuous sense. It builds on our initial working on learning and interpolating Green's functions using a manifold interpolation technique. The main idea is to learn a Green's function using Rational Neural Networks (Greenlearning), use our Python implementation of chebfun to learn a continuous Singular Value Expansion (SVE) for the bivariate Green's function, and then interpolate SVE on a manifold of Quasimatrices. Here's a small schematic to outline the first part of the process:
We use chebpy as a starting point to implement a Python version of chebfun. The necessary features of chebfun in 2-Dimensions have been implemented along with bug fixes for chebpy. The implementation for the Rational Neural Networks to learn Green's functions is done in Pytorch.
# Create folder for the virtual environment.
$ mkdir -p ~/.venvs #
# Create a new virtual environment for the chebgreen package.
$ python -m venv ~/.venvs/chebgreen
# Activate environment (every time you want to use the package).
$ source ~/.venvs/chebgreen/bin/activate$ cd chebgreen
# Install the package and its dependencies.
$ pip install . -r requirements.txtThe code uses MATLAB and the MATLAB library Chebfun to generate the datasets. Instructions for installation can be found here:
The package provides some MATLAB scripts in the scripts directory for data generation. One can also load a dataset generated from another simulation software or from experiments, the format for the datasets is specified in chebgreen/model.py.
The examples of using the package to learn and interpolate Green's function from a given Partial Differential Equation is inside Jupyter notebooks in examples directory. It also provides important visualizations for the learned Green's function, and computes an empirical error.