Work

Multiresolution Sobolev Trained Fourier Neural Operator for Cross-Resolution Surrogate Modelling of Parametric Two-Phase Darcy Flows in Porous Media

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.05188

Authors: Zhang, Zhao, Guo, Chengjin, Chen, Zhenglong, Zhang, Kai, Liu, Piyang, Yan, Xia

Institutions: Shandong University, China University of Petroleum, East China, Qingdao University of Technology

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Shandong University, Natural Science Foundation of Shandong Province, Fundamental Research Funds for the Central Universities

Award: G4007993853

OpenAlex ID: W7220703791

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