mlsanityData to 7 Oct 2026

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

arXiv 2109.03697 ↗First posted 3 Sep 2021physics.geo-ph cs.LGcited by 292

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Abstract (arXiv)

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.

Key facts. Cited by 292 papers in the map (data through 7 Oct 2026). Builds on 8 of its 45 references that are in the map. First posted on arXiv 3 Sep 2021.

Builds on

8 of 45 references.

References · 8

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  3. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  4. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  5. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  6. 2019A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problemscited by 59
  7. 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
  8. 2021CCSNet: a deep learning modeling suite for CO2 storagecited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 24; 2023: 60; 2024: 52; 2025: 78; 2026: 74.

292 papers.

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  1. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  2. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  3. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  4. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  5. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  6. 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 237
  7. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 225
  8. 2022U-NO: U-shaped Neural Operatorscited by 219
  9. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  10. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 128
  11. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  12. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observationcited by 100
38 more
  1. 2022Clifford Neural Layers for PDE Modelingcited by 91
  2. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  3. 2023Solving High-Dimensional PDEs with Latent Spectral Modelscited by 84
  4. 2023Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEscited by 66
  5. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  6. 2024Neural Operators with Localized Integral and Differential Kernelscited by 59
  7. 2023Improved Operator Learning by Orthogonal Attentioncited by 58
  8. 2023Towards Stability of Autoregressive Neural Operatorscited by 54
  9. 2022Generative Adversarial Neural Operatorscited by 51
  10. 2023Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestrationcited by 46
  11. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 45
  12. 2023Nonlocality and Nonlinearity Implies Universality in Operator Learningcited by 43
  13. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  14. 2023Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equationcited by 32
  15. 2023Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networkscited by 32
  16. 2024Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solverscited by 31
  17. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  18. 2023Physics informed WNOcited by 26
  19. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  20. 2022Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEscited by 25
  21. 2023Rethinking materials simulations: Blending direct numerical simulations with neural operatorscited by 25
  22. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  23. 2023Deep Operator Network Approximation Rates for Lipschitz Operatorscited by 24
  24. 2022Transformer Meets Boundary Value Inverse Problemscited by 22
  25. 2023Variational Autoencoding Neural Operatorscited by 22
  26. 2024VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Predictioncited by 22
  27. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  28. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  29. 2022Transform Once: Efficient Operator Learning in Frequency Domaincited by 20
  30. 2023Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domainscited by 20
  31. 2023Improved generalization with deep neural operators for engineering systems: Path towards digital twincited by 19
  32. 2024PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systemscited by 18
  33. 2022NeurOLight: A Physics-Agnostic Neural Operator Enabling Parametric Photonic Device Simulationcited by 17
  34. 2022Bounding the Rademacher Complexity of Fourier neural operatorscited by 16
  35. 2023PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformerscited by 16
  36. 2023Multi-scale Time-stepping of Partial Differential Equations with Transformerscited by 14
  37. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  38. 2025A multi-agentic framework for real-time, autonomous freeform metasurface designcited by 14

50 most cited of 292 All 292 (JSON)