This repository holds the code used in the paper "Operator learning for hyperbolic partial differential equations," available on the arXiv.
The figures used in the paper were generated with the default parameters in main.m. The code was run on a 64-core AMD Opteron with 512GB of RAM and a 16-core Xeon E5-2640 with 256GB of RAM, using MATLAB version 9.13.0.2105380 (R2022b), Update 2.
Our code requires chebfun, which is available for download here. Plotting some of the figures requires inpaint_nans, an interpolation function written by John D'Errico.
Simply place chebfun and inpaint_nans.m into the folder with the rest of the code. Add them to your path and run main.m. This runs Algorithm 2 of the aforementioned paper, saves all the relevant variables to a .mat file, and saves a figure containing three plots: 1) the approximate Green's function overlaid with partition blocks 2) the actual Green's function 3) the L2 error. Note: The code will attempt to run in parallel; to avoid this, replace the function CONSTRUCTPAR with CONSTRUCT in main.m. Arguments will need to be modified.
Several parameters are available for modification, all of which are described in main.m. In theory, the Green's function G can be replaced by any anonymous function with the same arguments and output.
To run the version of our algorithm that generates input-output data from a numerical solver (implemented in solve_uw1.m and solve_c2.m), run mainbb.m. All code files related to this "black-box" version has the suffix "...bb.m".
Our code is a proof-of-concept for a theoretical algorithm. It is not intended for real-world use for learning solution operators of hyperbolic PDEs.
Comments and suggestions welcome.