mlsanityData to 14 Oct 2026

Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness

arXiv 2305.17289 ↗First posted 26 May 2023cs.LG physics.comp-ph physics.geo-phcited by 60

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Abstract (arXiv)

Full waveform inversion (FWI) infers the subsurface structure information from seismic waveform data by solving a non-convex optimization problem. Data-driven FWI has been increasingly studied with various neural network architectures to improve accuracy and computational efficiency. Nevertheless, the applicability of pre-trained neural networks is severely restricted by potential discrepancies between the source function used in the field survey and the one utilized during training. Here, we develop a Fourier-enhanced deep operator network (Fourier-DeepONet) for FWI with the generalization of seismic sources, including the frequencies and locations of sources. Specifically, we employ the Fourier neural operator as the decoder of DeepONet, and we utilize source parameters as one input of Fourier-DeepONet, facilitating the resolution of FWI with variable sources. To test Fourier-DeepONet, we develop three new and realistic FWI benchmark datasets (FWI-F, FWI-L, and FWI-FL) with varying source frequencies, locations, or both. Our experiments demonstrate that compared with existing data-driven FWI methods, Fourier-DeepONet obtains more accurate predictions of subsurface structures in a wide range of source parameters. Moreover, the proposed Fourier-DeepONet exhibits superior robustness when handling data with Gaussian noise or missing traces and sources with Gaussian noise, paving the way for more reliable and accurate subsurface imaging across diverse real conditions.

Key facts. Cited by 60 papers in the map (data through 14 Oct 2026). Builds on 17 of its 45 references that are in the map. First posted on arXiv 26 May 2023.

Builds on

17 of 45 references.

References · 17

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  5. 2018Certified Robustness to Adversarial Examples with Differential Privacycited by 468
  6. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
  7. 2016Adversarial Training Methods for Semi-Supervised Text Classificationcited by 280
  8. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  9. 2019Robust Learning with Jacobian Regularizationcited by 129
  10. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  11. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  12. 2018InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFscited by 61
5 more
  1. 2023Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestrationcited by 46
  2. 2021OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversioncited by 44
  3. 2018Data-driven Seismic Waveform Inversion: A Study on the Robustness and Generalizationcited by 30
  4. 2021Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loopcited by 29
  5. 2023PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systemscited by 19

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 21; 2025: 17; 2026: 16.

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  1. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 46
  2. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  3. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  4. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  5. 2024LeMON: Learning to Learn Multi-Operator Networkscited by 14
  6. 2025AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learningcited by 14
  7. 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
  8. 2024Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestrationcited by 11
  9. 2023An Empirical Study of Large-Scale Data-Driven Full Waveform Inversioncited by 9
  10. 2024Speeding up and reducing memory usage for scientific machine learning via mixed precisioncited by 8
  11. 2024Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneitycited by 8
  12. 2025TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansioncited by 8
38 more
  1. 2025Temporal Neural Operator for Modeling Time-Dependent Physical Phenomenacited by 8
  2. 2023Scattering with Neural Operatorscited by 7
  3. 2024Learning Physics for Unveiling Hidden Earthquake Ground Motions via Conditional Generative Modelingcited by 7
  4. 2025PI-MFM: Physics-informed multimodal foundation model for solving partial differential equationscited by 7
  5. 2023A hybrid Decoder-DeepONet operator regression framework for unaligned observation datacited by 6
  6. 2024Paired Autoencoders for Likelihood-free Estimation in Inverse Problemscited by 6
  7. 2024A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problemscited by 6
  8. 2024Separable Operator Networkscited by 5
  9. 2024Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materialscited by 5
  10. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  11. 2025RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversioncited by 5
  12. 2024Resolution invariant deep operator network for PDEs with complex geometriescited by 4
  13. 2024Solving Partial Differential Equations in Different Domains by Operator Learning method Based on Boundary Integral Equationscited by 4
  14. 2025RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equationscited by 4
  15. 2023Neural Born Series Operator for Biomedical Ultrasound Computed Tomographycited by 3
  16. 2024Physics and geometry informed neural operator network with application to acoustic scatteringcited by 3
  17. 2025Coefficient-to-Basis Network: A Fine-Tunable Operator Learning Framework for Inverse Problems with Adaptive Discretizations and Theoretical Guaranteescited by 3
  18. 2026A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systemscited by 3
  19. 2026Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networkscited by 3
  20. 2023An Unsupervised Deep Learning Approach for the Wave Equation Inverse Problemcited by 2
  21. 2024General-Kindred Physics-Informed Neural Network to the Solutions of Singularly Perturbed Differential Equationscited by 2
  22. 2025GALDS: A Graph-Autoencoder-based Latent Dynamics Surrogate model to predict neurite material transportcited by 2
  23. 2025OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomographycited by 2
  24. 2025AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kineticscited by 2
  25. 2026Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operatorscited by 2
  26. 2026Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversioncited by 2
  27. 2024SG-DeepONet: Source-generalized deep operator learning for full waveform inversioncited by 1
  28. 2025Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)cited by 1
  29. 2025BEKAN: Boundary condition-guaranteed evolutionary Kolmogorov-Arnold networks with radial basis functions for solving PDE problemscited by 1
  30. 2026Hybrid operator learning of wave scattering maps in high-contrast mediacited by 1
  31. 2026Unveiling the Mechanism of Continuous Representation Full-Waveform Inversion: A Wave Based Neural Tangent Kernel Frameworkcited by 1
  32. 2026On the training of physics-informed neural operators for solving parametric partial differential equationscited by 1
  33. 2024A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous mediacited by 0
  34. 2024Radial Basis Operator Networkscited by 0
  35. 2024Survey of Deep Learning and Physics-Based Approaches in Computational Wave Imagingcited by 0
  36. 2025GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometriescited by 0
  37. 2025Machine Learning-Based Ultrasonic Weld Characterization Using Hierarchical Wave Modeling and Diffusion-Driven Distribution Alignmentcited by 0
  38. 2025SA-EMO: Structure-Aligned Encoder Mixture of Operators for Generalizable Full-waveform Inversioncited by 0

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