A Dual-Branch Coupled Fourier Neural Operator for High-Resolution Multi-Phase Flow Modeling in Porous Media
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water-17-03351-v2.pdf
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Author(s)
Al Hashim, Hassan
Elyas, Odai
Williams, John
Date Issued
November 22, 2025
Journal
Water
Publisher
Multidisciplinary Digital Publishing Institute
Citation
Al Hashim, H.; Elyas, O.; Williams, J. A Dual-Branch Coupled Fourier Neural Operator for High-Resolution Multi-Phase Flow Modeling in Porous Media. Water 2025, 17, 3351.
Version
Final published version
Abstract
This paper investigates a physics-informed surrogate modeling framework for multi-phase flow in porous media based on the Fourier Neural Operator. Traditional numerical simulators, though accurate, suffer from severe computational bottlenecks due to fine-grid discretizations and the iterative solution of highly nonlinear partial differential equations. By parameterizing the kernel integral directly in Fourier space, the operator provides a discretization-invariant mapping between function spaces, enabling efficient spectral convolutions. We introduce a Dual-Branch Adaptive Fourier Neural Operator with a shared Fourier encoder and two decoders: a saturation branch that uses an inverse Fourier transform followed by a multilayer perceptron and a pressure branch that uses a convolutional decoder. Temporal information is injected via Time2Vec embeddings and a causal temporal transformer, conditioning each forward pass on step index and time step to maintain consistent dynamics across horizons. Physics-informed losses couple data fidelity with residuals from mass conservation and Darcy pressure, enforcing the governing constraints in Fourier space; truncated spectral kernels promote generalization across meshes without retraining. On SPE10-style heterogeneities, the model shifts the infinity-norm error mass into the 10−2 to 10−1 band during early transients and sustains lower errors during pseudo-steady state. In zero-shot three-dimensional coarse-to-fine upscaling from 30 ×110 ×5 to 60 ×220 ×5, it attains 𝑅2 =0.90, RMSE = 4.4 ×10−2, and MAE = 3.2 ×10−2, with more than 90% of voxels below five percent absolute error across five unseen layers, while the end-to-end pipeline runs about three times faster than a full-order fine-grid solve and preserves water-flood fronts and channel connectivity. Benchmarking against established baselines indicates a scalable, high-fidelity alternative for high-resolution multi-phase flow simulation in porous media.
MIT Department
Massachusetts Institute of Technology. Center for Computational Science and Engineering
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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DOI of Published Version
https://doi.org/10.3390/w17233351
