This repository contains supplemental data for the article Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operators, accepted for publication in the International Journal for Numerical Methods in Engineering (IJNME) by Julius Herb and Felix Fritzen [1].

In this publication, we introduce UNO-CG, a hybrid solver that accelerates conjugate gradient (CG) solvers using specially designed machine-learned preconditioners, while ensuring convergence by construction. As a preconditioner, we propose Unitary Neural Operators (UNOs) as a modification of the established Fourier Neural Operators. Our method can be interpreted as a data-driven discovery of Green's functions, which are then used much like expert knowledge to accelerate iterative solvers.

The data contained in this DaRUS repository acts as an extension to the GitHub repository that contains a software package for UNO-CG, including a GPU-accelerated implementation of the hybrid solver in PyTorch, an implementation for PETSc, and the training procedures proposed in our article.

All results and figures in the article can be reproduced using the mentioned software package together with the data sets available in this DaRUS repository. As part of the training data and evaluation data, we consider bi-phasic two-dimensional microstructures with a resolution of 400 × 400 pixels, as published in [2], and three-dimensional microstructures with a resolution of 192 × 192 × 192 voxels, as published in [3]. Further information is available in the README.md file of this repository.

[1] Herb, J. and Fritzen, F. (2026), Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operators. Int J Numer Methods Eng. https://doi.org/10.1002/nme.70277

[2] Lißner, J. (2020). 2d microstructure data (Version V2) [dataset]. DaRUS. https://doi.org/10.18419/DARUS-1151

[3] Prifling, B., Röding, M., Townsend, P., Neumann, M., and Schmidt, V. (2020). Large-scale statistical learning for mass transport prediction in porous materials using 90,000 artificially generated microstructures [dataset]. Zenodo. https://doi.org/10.5281/zenodo.4047774

The related publication was accepted by IJNME on 2026-01-22 and will be available online soon.