mlsanityData to 14 Oct 2026

Geometry-Informed Neural Operator Transformer

arXiv 2504.19452 ↗First posted 28 Apr 2025cs.LG physics.comp-phcited by 8

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Abstract (arXiv)

Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations. This work introduces the Geometry-Informed Neural Operator Transformer (GINOT), which integrates the transformer architecture with the neural operator framework to enable forward predictions on arbitrary geometries. GINOT employs a sampling and grouping strategy together with an attention mechanism to encode surface point clouds that are unordered, exhibit non-uniform point densities, and contain varying numbers of points for different geometries. The geometry information is seamlessly integrated with query points in the solution decoder through the attention mechanism. The performance of GINOT is validated on multiple challenging datasets, showcasing its high accuracy and strong generalization capabilities for complex and arbitrary 2D and 3D geometries.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 26 of its 41 references that are in the map. First posted on arXiv 28 Apr 2025.

Builds on

26 of 41 references.

References · 26

  1. 2017Attention Is All You Needcited by 60,361
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
  3. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,401
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  5. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  6. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 819
  7. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  8. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  9. 2021Choose a Transformer: Fourier or Galerkincited by 343
  10. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
  11. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 303
  12. 2022Transformer for Partial Differential Equations' Operator Learningcited by 283
14 more
  1. 2022Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modelingcited by 65
  2. 2023Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loadscited by 47
  3. 2024Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometriescited by 47
  4. 2020Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithmscited by 34
  5. 2023Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loadscited by 33
  6. 2023Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionalscited by 26
  7. 2023OceanNet: A principled neural operator-based digital twin for regional oceanscited by 24
  8. 2023Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutionscited by 22
  9. 2022PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equationscited by 21
  10. 2023Improved generalization with deep neural operators for engineering systems: Path towards digital twincited by 19
  11. 2024Physics-Informed Geometry-Aware Neural Operatorcited by 19
  12. 2024DeepJEB: 3D Deep Learning-based Synthetic Jet Engine Bracket Datasetcited by 16
  13. 2024Physics-informed Discretization-independent Deep Compositional Operator Networkcited by 6
  14. 2024Univariate Conditional Variational Autoencoder for Morphogenic Patterns Design in Frontal Polymerization-Based Manufacturingcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 5.

8 papers.

  1. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 23
  2. 2025Multi-Level Monte Carlo Training of Neural Operatorscited by 4
  3. 2026Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flowscited by 3
  4. 2025Geometric Laplace Neural Operatorcited by 2
  5. 2026GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domainscited by 1
  6. 2026LEIA: Learned Environment for Interactive Architected Materialscited by 0
  7. 2026FLARE++: Low-rank attention with dynamic attention routingcited by 0
  8. 2026CANTO: CAD-Native Transformer Operators for AI-Aided Engineeringcited by 0