mlsanityData to 7 Oct 2026

A hybrid Decoder-DeepONet operator regression framework for unaligned observation data

arXiv 2308.09274 ↗First posted 18 Aug 2023cs.LGcited by 6

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Abstract (arXiv)

Deep neural operators (DNOs) have been utilized to approximate nonlinear mappings between function spaces. However, DNOs face the challenge of increased dimensionality and computational cost associated with unaligned observation data. In this study, we propose a hybrid Decoder-DeepONet operator regression framework to handle unaligned data effectively. Additionally, we introduce a Multi-Decoder-DeepONet, which utilizes an average field of training data as input augmentation. The consistencies of the frameworks with the operator approximation theory are provided, on the basis of the universal approximation theorem. Two numerical experiments, Darcy problem and flow-field around an airfoil, are conducted to validate the efficiency and accuracy of the proposed methods. Results illustrate the advantages of Decoder-DeepONet and Multi-Decoder-DeepONet in handling unaligned observation data and showcase their potentials in improving prediction accuracy.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 23 of its 59 references that are in the map. First posted on arXiv 18 Aug 2023.

Builds on

23 of 59 references.

References · 23

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  4. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  5. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  6. 2019Machine Learning for Fluid Mechanicscited by 380
  7. 2017PDE-Net: Learning PDEs from Datacited by 304
  8. 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 208
  9. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  10. 2022MIONet: Learning multiple-input operators via tensor productcited by 180
  11. 2019Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networkscited by 144
  12. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
11 more
  1. 2022Deep transfer operator learning for partial differential equations under conditional shiftcited by 83
  2. 2022Learning two-phase microstructure evolution using neural operators and autoencoder architecturescited by 72
  3. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  4. 2022Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problemscited by 47
  5. 2022Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priorscited by 39
  6. 2021Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural networkcited by 35
  7. 2023Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loadscited by 33
  8. 2021Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEscited by 22
  9. 2019Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flowscited by 21
  10. 2023Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoilscited by 19
  11. 2019Machine learning for protein folding and dynamicscited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 3; 2026: 1.

6 papers.

  1. 2025Machine learning for modelling unstructured grid data in computational physics: a reviewcited by 12
  2. 2024BI-EqNO: Generalized Approximate Bayesian Inference with an Equivariant Neural Operator Frameworkcited by 5
  3. 2024Global 4D Ionospheric STEC Prediction based on DeepONet for GNSS Rayscited by 1
  4. 2025Invertible Koopman neural operator for data-driven modeling of partial differential equationscited by 1
  5. 2026Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equationscited by 1
  6. 2025An Interpretable Operator-Learning Model for Electric Field Profile Reconstruction in Discharges Based on the EFISH Methodcited by 0