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Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration

arXiv 2303.04778 ↗First posted 8 Mar 2023cs.LG physics.comp-phcited by 46

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Abstract (arXiv)

Geologic carbon sequestration (GCS) is a safety-critical technology that aims to reduce the amount of carbon dioxide in the atmosphere, which also places high demands on reliability. Multiphase flow in porous media is essential to understand CO2 migration and pressure fields in the subsurface associated with GCS. However, numerical simulation for such problems in 4D is computationally challenging and expensive, due to the multiphysics and multiscale nature of the highly nonlinear governing partial differential equations (PDEs). It prevents us from considering multiple subsurface scenarios and conducting real-time optimization. Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the recently developed framework of the multiple-input deep neural operators (MIONet) and incorporates the Fourier neural operator (FNO) in the network architecture. Once Fourier-MIONet is trained, it can predict the evolution of saturation and pressure of the multiphase flow under various reservoir conditions, such as permeability and porosity heterogeneity, anisotropy, injection configurations, and multiphase flow properties. Compared to the enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown parameters, and it can be trained in significantly less time (about 3.5 times faster) with much lower CPU memory (< 15%) and GPU memory (< 35%) requirements, to achieve similar prediction accuracy. In addition to the lower computational cost, Fourier-MIONet can be trained with only 6 snapshots of time to predict the PDE solutions for 30 years. The excellent generalizability of Fourier-MIONet is enabled by its adherence to the physical principle that the solution to a PDE is continuous over time.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). Builds on 21 of its 75 references that are in the map. First posted on arXiv 8 Mar 2023.

Builds on

21 of 75 references.

References · 21

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  5. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  6. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  7. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  8. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  9. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
  10. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
  11. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  12. 2022MIONet: Learning multiple-input operators via tensor productcited by 180
9 more
  1. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  2. 2022NOMAD: Nonlinear Manifold Decoders for Operator Learningcited by 81
  3. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  4. 2019A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problemscited by 59
  5. 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
  6. 2022Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problemscited by 47
  7. 2021One-shot learning for solution operators of partial differential equationscited by 27
  8. 2022Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networkscited by 23
  9. 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: 2023: 6; 2024: 15; 2025: 17; 2026: 8.

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  1. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  2. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 45
  3. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  4. 2024VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Predictioncited by 22
  5. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 19
  6. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  7. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  8. 2024A hybrid iterative method based on MIONet for PDEs: Theory and numerical examplescited by 13
  9. 2024LeMON: Learning to Learn Multi-Operator Networkscited by 13
  10. 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
  11. 2024Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestrationcited by 11
  12. 2025Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEscited by 9
34 more
  1. 2024Speeding up and reducing memory usage for scientific machine learning via mixed precisioncited by 8
  2. 2024Multiple-Input Fourier Neural Operator (MIFNO) for source-dependent 3D elastodynamicscited by 8
  3. 2024Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneitycited by 8
  4. 2025Temporal Neural Operator for Modeling Time-Dependent Physical Phenomenacited by 8
  5. 2023Scattering with Neural Operatorscited by 7
  6. 2025TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansioncited by 7
  7. 2025A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theorycited by 6
  8. 2025PI-MFM: Physics-informed multimodal foundation model for solving partial differential equationscited by 6
  9. 2023History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterizationcited by 5
  10. 2025RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversioncited by 5
  11. 2023A Critical Review of Physics-Informed Machine Learning Applications in Subsurface Energy Systemscited by 4
  12. 2024Separable Operator Networkscited by 4
  13. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  14. 2024Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogatescited by 3
  15. 2025Fourier Neural Operator based surrogates for CO2 storage in realistic geologiescited by 3
  16. 2026Graph In-Context Operator Networks for Generalizable Spatiotemporal Predictioncited by 3
  17. 2026A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systemscited by 3
  18. 2023Understanding the Efficacy of U-Net & Vision Transformer for Groundwater Numerical Modellingcited by 2
  19. 2025Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systemscited by 2
  20. 2024Harnessing physics-informed operators for high-dimensional reliability analysis problemscited by 1
  21. 2025Physics-informed Attention-enhanced Fourier Neural Operator for Solar Magnetic Field Extrapolationscited by 1
  22. 2025Autoregressive Surrogate Modeling of the Solar Wind with Spherical Fourier Neural Operatorcited by 1
  23. 2026Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networkscited by 1
  24. 2024A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous mediacited by 0
  25. 2024Radial Basis Operator Networkscited by 0
  26. 2025Learning multi-phase flow and transport in fractured porous media with auto-regressive and recurrent graph neural networkscited by 0
  27. 2025FFINO: Factorized Fourier Improved Neural Operator for Modeling Multiphase Flow in Underground Hydrogen Storagecited by 0
  28. 2025Operator Learning for Consolidation: An Architectural Comparison for DeepONet Variantscited by 0
  29. 2025Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injurycited by 0
  30. 2026LAViG-FLOW: Latent Autoregressive Video Generation for Fluid Flow Simulationscited by 0
  31. 2026pADAM: A Plug-and-Play All-in-One Diffusion Architecture for Multi-Physics Learningcited by 0
  32. 2026Nested Fourier-enhanced neural operator for efficient modeling of radiation transfer in firescited by 0
  33. 2026UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learningcited by 0
  34. 2026Diffusion-corrected Autoregressive Fourier Neural Operator for Droplet Evolution Predictioncited by 0