Operator learning using random features: a tool for scientific computing

Description

This repository contains the datasets corresponding to the two benchmark problems appearing in the SIAM papers "The Random Feature Model for Input-Output Maps between Banach Spaces" [SIAM J. Sci. Comput., Vol. 43, No. 5 (2021), pp. A3212–A3243] and the paper "Operator learning using random features: a tool for scientific computing" [SIAM Review, Vol. 66, No. 3 (2024), pp. 535–571].

The first file is the data for the viscous Burgers' equation problem. It contains Python Numpy files "train.npy" and "test.npy" that each contain both the inputs and outputs of the 1D benchmark. The other files collect the parameters that define the benchmark as explained in the papers.

The second file is for steady Darcy flow problem. It contains a MATLAB data file "data.mat" that stores the inputs and outputs of the 2D problem for both the train and test sets, as well as a file "params.mat" that stores the values of the parameters that define the benchmark.

The code associated with these data may be found at:
https://github.com/nickhnelsen/random-features-banach
https://github.com/nickhnelsen/error-bounds-for-vvRF

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