U-FNO - an enhanced Fourier neural operator based-deep learning model for multiphase flow

By Gege Wen, Zong-Yi Li, Kamyar Azizzadenesheli, Anima Anandkumar, Sally M. Benson. Advances in Water Resources, 2021

683 citations recorded by the source corpus.

Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we present U-FNO, a novel neural network architecture for solving multiphase flow problems with superior accuracy, speed, and data efficiency. U-FNO is designed based on the newly proposed Fourier neural operator (FNO), which has shown excellent performance in single-phase flows. We extend the FNO-based architecture to a highly complex CO2-water multiphase problem with wide ranges of permeability and porosity heterogeneity, anisotropy, reservoir conditions, injection configurations, flow rates, and multiphase flow properties. The U-FNO architecture is more accurate in gas saturation and pressure buildup predictions than the original FNO and a state-of-the-art convolutional neural network (CNN) benchmark. Meanwhile, it has superior data utilization efficiency, requiring only a third of the training data to achieve the equivalent accuracy as CNN. U-FNO provides superior performance in highly heterogeneous geological formations and critically important applications such as gas saturation and pressure buildup"fronts"determination. The trained model can serve as a general-purpose alternative to routine numerical simulations of 2D-radial CO2 injection problems with significant speed-ups than traditional simulators.

Subfields: Aerospace Engineering, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bd1a1cea6fab16c00e3519745ff798195332fcdd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere (2023, background): “, 2020) and their variants (Guibas et al., 2021; Wen et al., 2022; Rahman et al., 2022; Kovachki et al., 2023; Kossaifi et al., 2023) possess the advantage of learning mappings between function spaces, which act globally on the entire domain.”
Transformer for Partial Differential Equations' Operator Learning (2022, background): “The promising features of data-driven operator learning, in particular the generalization capability within a family of PDE and the potential adaptivity to different discretizations, have given rise to a wide array of recent research works [5, 9, 10, 23, 32, 41, 42, 46, 53, 61, 86].”
Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, background): “A possible idea could be to apply Fourier neural operator (FNO) (Wen et al, 2022), in order to learn a generalized functional space (Rafiq et al, 2022).”
GNOT: A General Neural Operator Transformer for Operator Learning (2023, background): “Some works also propose variants of FNO from other aspects (Gupta et al., 2021; Wen et al., 2022; Tran et al., 2021).”
Transolver: A Fast Transformer Solver for PDEs on General Geometries (2024, methodology): “Afterward, U-NO (Rahman et al., 2023) and U-FNO (Wen et al., 2022) are presented by plugging the FNO with U-Net (Ronneberger et al., 2015) for multiscale modeling.”
Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers (2021, background): “To compensate local features and non-periodic boundaries, we can add a residual term x m,n (can also be parameterized as a simple local convolution) to the token demixing step 3 in FNO; see also Wen et al. (2021).”
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries (2022, methodology): “When applying it to irregular domain shapes, previous works usually embed the domain into a larger rectangular domain [16].”