https://github.com/nickhnelsen/error-bounds-for-vvrf
Code for the paper ``Error Bounds for Learning with Vector-Valued Random Features''
https://github.com/nickhnelsen/error-bounds-for-vvrf
fourier-neural-operator functional-regression infinite-dimensions neural-operator operator-learning partial-differential-equations random-features
Last synced: about 2 months ago
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Code for the paper ``Error Bounds for Learning with Vector-Valued Random Features''
- Host: GitHub
- URL: https://github.com/nickhnelsen/error-bounds-for-vvrf
- Owner: nickhnelsen
- License: mit
- Created: 2023-08-02T19:30:38.000Z (almost 2 years ago)
- Default Branch: main
- Last Pushed: 2024-08-08T11:38:45.000Z (9 months ago)
- Last Synced: 2024-08-08T13:47:08.383Z (9 months ago)
- Topics: fourier-neural-operator, functional-regression, infinite-dimensions, neural-operator, operator-learning, partial-differential-equations, random-features
- Language: Python
- Homepage: https://proceedings.neurips.cc/paper_files/paper/2023/hash/e34d908241aef40440e61d2a27715424-Abstract-Conference.html
- Size: 76.2 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Code for the 2023 NeurIPS Spotlight paper ``Error Bounds for Learning with Vector-Valued Random Features''
## Installation
The command
```
conda env create -f Project.yml
```
creates an environment called ``operator``. [PyTorch](https://pytorch.org/) will be installed in this step.
Activate the environment with
```
conda activate operator
```
and deactivate with
```
conda deactivate
```
## Data
The 1D viscous Burgers' equation dataset is a standard operator learning benchmark first introduced in [Nelsen and Stuart 2021](https://arxiv.org/abs/2005.10224).
The particular setup used in this example comes from [zongyi-li/fourier_neural_operator](https://github.com/zongyi-li/fourier_neural_operator) and is found below:
* [Burgers' dataset](https://drive.google.com/drive/folders/1UnbQh2WWc6knEHbLn-ZaXrKUZhp7pjt-?usp=sharing)
Please download ``Burgers_R10.zip`` which contains the dataset file ``burgers_data_R10.mat``. There are $2048$ input-outpairs at spatial resolution $8192$.
## Running the example
In the script ``train.py``, assign in the variable ``data_path`` the global path to the data file ``burgers_data_R10.mat``.
The example may then be run as
```
python -u train.py M N J 0 lambda my_path
```
where
* ``M`` is the number of random features,
* ``N`` is the number of training data pairs,
* ``J`` is the desired spatial resolution for training and testing.
* ``lambda`` is the regularization parameter
* ``my_path`` is the output directory
The code defaults to running on GPU, if one is available.
## References
- [Error Bounds for Learning with Vector-Valued Random Features](https://arxiv.org/abs/2305.17170)
- [The Random Feature Model for Input-Output Maps between Banach Spaces](https://arxiv.org/abs/2005.10224)
- [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)