https://github.com/nickhnelsen/random-features-banach
Code for the paper "The Random Feature Model for Input-Output Maps between Banach Spaces"
https://github.com/nickhnelsen/random-features-banach
fourier-neural-operator functional-regression infinite-dimensions neural-operator operator-learning partial-differential-equations random-features
Last synced: about 2 months ago
JSON representation
Code for the paper "The Random Feature Model for Input-Output Maps between Banach Spaces"
- Host: GitHub
- URL: https://github.com/nickhnelsen/random-features-banach
- Owner: nickhnelsen
- License: mit
- Created: 2024-03-16T02:47:30.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2024-08-08T11:36:52.000Z (9 months ago)
- Last Synced: 2024-08-08T13:45:56.395Z (9 months ago)
- Topics: fourier-neural-operator, functional-regression, infinite-dimensions, neural-operator, operator-learning, partial-differential-equations, random-features
- Language: Python
- Homepage: https://doi.org/10.22002/55tdh-hda68
- Size: 19.7 MB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# random-features-banach
This repository contains the code associated with the journal articles "The Random Feature Model for Input-Output Maps between Banach Spaces" ([SIAM J. Sci. Comput., Vol. 43, No. 5 (2021), pp. A3212–A3243](https://doi.org/10.1137/20M133957X)) and "Operator learning using random features: a tool for scientific computing" ([SIAM Review, Vol. 66, No. 3 (2024), pp. 535–571](https://doi.org/10.1137/24M1648703)). It implements the function-valued random features method for two operator learning benchmark problems: 1) the solution operator of 1D viscous Burgers' equation and 2) the solution operator of the 2D Darcy flow elliptic partial differential equation.
> [!IMPORTANT]
> A more efficient and up-to-date GPU implementation of this code is available at:
>
> https://github.com/nickhnelsen/error-bounds-for-vvRF
>
> We recommend that users interested in the operator random features method migrate over to that repository. The current repo `random-features-banach` should only be used to reproduce the results in the journal papers and not used for future developements.
## Requirements
* Python 3
* Numpy
* Numba
* Scipy
* Matplotlib
## Data
The data may be downloaded at [](https://doi.org/10.22002/55tdh-hda68), which contains two `*.zip` files:
1. `burgers`: input-output data as Python `*.npy` files.
2. `darcy`: input-output data as MATLAB `*.mat` files.
```
Nelsen, N. H. & Stuart, A.M. (2024). Operator learning using random features: a tool for scientific computing [Data set]. CaltechDATA. https://doi.org/10.22002/55tdh-hda68. Mar. 15, 2024.
```
## References
The main reference that explains the two benchmark problems is the paper ``[The Random Feature Model for Input-Output Maps between Banach Spaces](https://arxiv.org/abs/2005.10224)'' by Nicholas H. Nelsen and Andrew M. Stuart. Other relevant references include:
- [Error Bounds for Learning with Vector-Valued Random Features](https://arxiv.org/abs/2305.17170)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://arxiv.org/abs/2010.08895)
- [Operator learning using random features: a tool for scientific computing](https://doi.org/10.1137/24M1648703)
## Citing
If you use `random-features-banach` in an academic paper, please cite the main references as follows:
```
@article{nelsen2021random,
title={The random feature model for input-output maps between Banach spaces},
author={Nelsen, Nicholas H. and Stuart, Andrew M.},
journal={SIAM Journal on Scientific Computing},
volume={43},
number={5},
pages={A3212--A3243},
year={2021},
publisher={Society for Industrial and Applied Mathematics},
doi = {10.1137/20M133957X}
}
@article{nelsen2024operator,
title={Operator learning using random features: a tool for scientific computing},
author={Nelsen, Nicholas H. and Stuart, Andrew M.},
journal={SIAM Review},
volume={66},
number={3},
pages={535--571},
year={2024},
month={8},
publisher={Society for Industrial and Applied Mathematics},
doi={10.1137/24M1648703}
}
```