mlsanityData to 7 Oct 2026

Variable-Input Deep Operator Networks

arXiv 2205.11404 ↗First posted 23 May 2022cs.LG cs.NA math.NAcited by 24

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Abstract (arXiv)

Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their applicability. We address this issue by proposing a novel operator learning framework, termed Variable-Input Deep Operator Network (VIDON), which allows for random sensors whose number and locations can vary across samples. VIDON is invariant to permutations of sensor locations and is proved to be universal in approximating a class of continuous operators. We also prove that VIDON can efficiently approximate operators arising in PDEs. Numerical experiments with a diverse set of PDEs are presented to illustrate the robust performance of VIDON in learning operators.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 18 of its 29 references that are in the map. First posted on arXiv 23 May 2022.

Builds on

18 of 29 references.

References · 18

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2017Deep Setscited by 1,394
  4. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  5. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
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  9. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  10. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
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6 more
  1. 2019Attentive Neural Processescited by 280
  2. 2018Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networkscited by 129
  3. 2019On the Limitations of Representing Functions on Setscited by 89
  4. 2022Learning Operators with Coupled Attentioncited by 88
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  6. 2018A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equationscited by 55

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 8; 2024: 4; 2025: 7; 2026: 2.

24 papers.

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  1. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  2. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 207
  3. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
  4. 2024Operator Learning: Algorithms and Analysiscited by 84
  5. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
  6. 2023Neural Inverse Operators for Solving PDE Inverse Problemscited by 61
  7. 2023Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learningcited by 57
  8. 2023Operator learning with PCA-Net: upper and lower complexity boundscited by 44
  9. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  10. 2023HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetworkcited by 25
  11. 2023Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domainscited by 20
  12. 2022Variationally Mimetic Operator Networkscited by 19
12 more
  1. 2024Space-Time Continuous PDE Forecasting using Equivariant Neural Fieldscited by 18
  2. 2023Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific MLcited by 8
  3. 2024Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular gridscited by 7
  4. 2025ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machinescited by 3
  5. 2025Deep Neural ODE Operator Networks for PDEscited by 3
  6. 2025StFT: Spatio-temporal Fourier Transformer for Long-term Dynamics Predictioncited by 1
  7. 2025SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Samplingcited by 1
  8. 2025Deep set based operator learning with uncertainty quantificationcited by 1
  9. 2026BLISSNet: Deep Operator Learning for Fast and Accurate Flow Reconstruction from Sparse Sensor Measurementscited by 1
  10. 2025DETNO: A Diffusion-Enhanced Transformer Neural Operator for Long-Term Traffic Forecastingcited by 0
  11. 2025In-Context Multi-Operator Learning with DeepOSetscited by 0
  12. 2026Deep operator learning for efficient sampling from invariant measures of stochastic differential equationscited by 0