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 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.

The particular setup used in this example comes from zongyi-li/fourier_neural_operator and is found below:

• Burgers' dataset

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
• The Random Feature Model for Input-Output Maps between Banach Spaces
• Fourier Neural Operator for Parametric Partial Differential Equations
• Operator Learning Using Random Features: A Tool for Scientific Computing