mlsanityData to 14 Oct 2026

Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration

arXiv 2409.16572 ↗First posted 25 Sep 2024cs.LG physics.comp-phcited by 11

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Abstract (arXiv)

Geological carbon sequestration (GCS) involves injecting CO2 into subsurface geological formations for permanent storage. Numerical simulations could guide decisions in GCS projects by predicting CO2 migration pathways and the pressure distribution in storage formation. However, these simulations are often computationally expensive due to highly coupled physics and large spatial-temporal simulation domains. Surrogate modeling with data-driven machine learning has become a promising alternative to accelerate physics-based simulations. Among these, the Fourier neural operator (FNO) has been applied to three-dimensional synthetic subsurface models. Here, to further improve performance, we have developed a nested Fourier-DeepONet by combining the expressiveness of the FNO with the modularity of a deep operator network (DeepONet). This new framework is twice as efficient as a nested FNO for training and has at least 80% lower GPU memory requirement due to its flexibility to treat temporal coordinates separately. These performance improvements are achieved without compromising prediction accuracy. In addition, the generalization and extrapolation ability of nested Fourier-DeepONet beyond the training range has been thoroughly evaluated. Nested Fourier-DeepONet outperformed the nested FNO for extrapolation in time with more than 50% reduced error. It also exhibited good extrapolation accuracy beyond the training range in terms of reservoir properties, number of wells, and injection rate.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 22 of its 50 references that are in the map. First posted on arXiv 25 Sep 2024.

Builds on

22 of 50 references.

References · 22

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  4. 2021Physics-informed neural networks with hard constraints for inverse designcited by 280
  5. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  6. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 222
  7. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  8. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  9. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  10. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  11. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  12. 2019A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problemscited by 59
10 more
  1. 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
  2. 2022Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operatorscited by 47
  3. 2023Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestrationcited by 46
  4. 2021One-shot learning for solution operators of partial differential equationscited by 30
  5. 2022Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networkscited by 23
  6. 2023PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systemscited by 19
  7. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  8. 2021CCSNet: a deep learning modeling suite for CO2 storagecited by 13
  9. 2024Speeding up and reducing memory usage for scientific machine learning via mixed precisioncited by 8
  10. 2023Deep Learning for Solving and Estimating Dynamic Macro-Finance Modelscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 8; 2026: 2.

11 papers.

  1. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 20
  2. 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
  3. 2024DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuningcited by 11
  4. 2025TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansioncited by 8
  5. 2025Temporal Neural Operator for Modeling Time-Dependent Physical Phenomenacited by 8
  6. 2025PI-MFM: Physics-informed multimodal foundation model for solving partial differential equationscited by 7
  7. 2025RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversioncited by 5
  8. 2025RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equationscited by 4
  9. 2026Adaptive Physics Transformer with Fused Global-Local Attention for Subsurface Energy Systemscited by 1
  10. 2025Learning multi-phase flow and transport in fractured porous media with auto-regressive and recurrent graph neural networkscited by 0
  11. 2026Nested Fourier-enhanced neural operator for efficient modeling of radiation transfer in firescited by 0