Multiresolution Sobolev Trained Fourier Neural Operator for Cross-Resolution Surrogate Modelling of Parametric Two-Phase Darcy Flows in Porous Media
Abstract
Surrogate modelling is important to enhance the computational efficiency of uncertainty quantification for physical processes involving random parameters. The advantage of Fourier neural operator (FNO) compared to conventional surrogates is its cross-resolution prediction capability. In the current study, a cross-resolution surrogate based on FNO is built for two-phase transient Darcy flows in porous media with random parameters. A multiresolution Sobolev learning method is proposed for FNO to enhance the cross-resolution prediction accuracy by incorporating first and second-order gradients in the loss function using training samples of different resolutions. The gradients are approximated by resolution-related finite difference schemes compatible with the grid for numerical simulation. Experimental results demonstrate the effectiveness of the new method in training FNO for building cross-resolution surrogates.
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BibTeX
@misc{zhang2026multiresolution,
title = {{Multiresolution Sobolev Trained Fourier Neural Operator for Cross-Resolution Surrogate Modelling of Parametric Two-Phase Darcy Flows in Porous Media}},
author = {Zhao Zhang and Chengjin Guo and Zhenglong Chen and Kai Zhang and Piyang Liu and Xia Yan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05188},
eprint = {2610.05188},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05188},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multiresolution Sobolev Trained Fourier Neural Operator for Cross-Resolution Surrogate Modelling of Parametric Two-Phase Darcy Flows in Porous Media
AU - Zhao Zhang
AU - Chengjin Guo
AU - Zhenglong Chen
AU - Kai Zhang
AU - Piyang Liu
AU - Xia Yan
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05188
UR - https://arxiv.org/abs/2610.05188
AB - Surrogate modelling is important to enhance the computational efficiency of uncertainty quantification for physical processes involving random parameters. The advantage of Fourier neural operator (FNO) compared to conventional surrogates is its cross-resolution prediction capability. In the current study, a cross-resolution surrogate based on FNO is built for two-phase transient Darcy flows in porous media with random parameters. A multiresolution Sobolev learning method is proposed for FNO to enhance the cross-resolution prediction accuracy by incorporating first and second-order gradients in the loss function using training samples of different resolutions. The gradients are approximated by resolution-related finite difference schemes compatible with the grid for numerical simulation. Experimental results demonstrate the effectiveness of the new method in training FNO for building cross-resolution surrogates.
ER -