mlsanityData to 7 Oct 2026

ViTO: Vision Transformer-Operator

arXiv 2303.08891 ↗First posted 15 Mar 2023cs.CV cs.NA math.NAcited by 29

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Abstract (arXiv)

We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply ViTO to solve inverse PDE problems of increasing complexity, namely for the wave equation, the Navier-Stokes equations and the Darcy equation. We focus on the more challenging case of super-resolution, where the input dataset for the inverse problem is at a significantly coarser resolution than the output. The results we obtain are comparable or exceed the leading operator network benchmarks in terms of accuracy. Furthermore, ViTO`s architecture has a small number of trainable parameters (less than 10% of the leading competitor), resulting in a performance speed-up of over 5x when averaged over the various test cases.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Builds on 24 of its 38 references that are in the map. First posted on arXiv 15 Mar 2023.

Builds on

24 of 38 references.

References · 24

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12 more
  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
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  7. 2021Choose a Transformer: Fourier or Galerkincited by 333
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  11. 2021ViT-V-Net: Vision Transformer for Unsupervised Volumetric Medical Image Registrationcited by 87
  12. 2022Transformer Meets Boundary Value Inverse Problemscited by 22

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 7; 2024: 8; 2025: 10; 2026: 4.

29 papers.

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  1. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  2. 2023Improved Operator Learning by Orthogonal Attentioncited by 58
  3. 2024Continuum Attention for Neural Operatorscited by 39
  4. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 20
  5. 2023Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO)cited by 16
  6. 2025Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Trainingcited by 10
  7. 2023MyCrunchGPT: A chatGPT assisted framework for scientific machine learningcited by 8
  8. 2024Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problemcited by 8
  9. 2025Transformer learns the cross-task prior and regularization for in-context learningcited by 7
  10. 2023About optimal loss function for training physics-informed neural networks under respecting causalitycited by 6
  11. 2024Separable Physics-Informed Neural Networks for the solution of elasticity problemscited by 5
  12. 2024Separable Operator Networkscited by 4
17 more
  1. 2025Learning Causal Graphs at Scale: A Foundation Model Approachcited by 4
  2. 2023Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materialscited by 3
  3. 2024Brain Tumor Classification using Vision Transformer with Selective Cross-Attention Mechanism and Feature Calibrationcited by 3
  4. 2025Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulatorscited by 3
  5. 2023Understanding the Efficacy of U-Net & Vision Transformer for Groundwater Numerical Modellingcited by 2
  6. 2024ODE-DPS: ODE-based Diffusion Posterior Sampling for Inverse Problems in Partial Differential Equationcited by 2
  7. 2025Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systemscited by 2
  8. 2025FA-INR: Adaptive Implicit Neural Representations for Interpretable Exploration of Simulation Ensemblescited by 1
  9. 2026In Transformer We Trust? A Perspective on Transformer Architecture Failure Modescited by 1
  10. 2026NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Trainingcited by 1
  11. 2024Harnessing The Power of Attention For Patch-Based Biomedical Image Classificationcited by 0
  12. 2024Prion-ViT: Prions-Inspired Vision Transformers for Temperature prediction with Specklegramscited by 0
  13. 2025Skin Cancer Classification: Hybrid CNN-Transformer Models with KAN-Based Fusioncited by 0
  14. 2025Efficient High-Accuracy PDEs Solver with the Linear Attention Neural Operatorcited by 0
  15. 2025Application of Graph Based Vision Transformers Architectures for Accurate Temperature Prediction in Fiber Specklegram Sensorscited by 0
  16. 2026Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approachcited by 0
  17. 2026LLT: Local Linear Transformer for PDE Operator Learningcited by 0