# Geometry-Informed Neural Operator Transformer

arXiv: https://arxiv.org/abs/2504.19452 · HTML: https://mlsanity.com/paper/2504.19452/

## 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 (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling](https://mlsanity.com/paper/2203.08205/) (2022)
- [Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads](https://mlsanity.com/paper/2306.08218/) (2023)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithms](https://mlsanity.com/paper/2004.10710/) (2020)
- [Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads](https://mlsanity.com/paper/2306.03645/) (2023)
- [Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals](https://mlsanity.com/paper/2302.13368/) (2023)
- [OceanNet: A principled neural operator-based digital twin for regional oceans](https://mlsanity.com/paper/2310.00813/) (2023)
- [Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions](https://mlsanity.com/paper/2308.07523/) (2023)
- [PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations](https://mlsanity.com/paper/2203.11363/) (2022)
- [Improved generalization with deep neural operators for engineering systems: Path towards digital twin](https://mlsanity.com/paper/2301.06701/) (2023)
- [Physics-Informed Geometry-Aware Neural Operator](https://mlsanity.com/paper/2408.01600/) (2024)
- [DeepJEB: 3D Deep Learning-based Synthetic Jet Engine Bracket Dataset](https://mlsanity.com/paper/2406.09047/) (2024)
- [Physics-informed Discretization-independent Deep Compositional Operator Network](https://mlsanity.com/paper/2404.13646/) (2024)
- [Univariate Conditional Variational Autoencoder for Morphogenic Patterns Design in Frontal Polymerization-Based Manufacturing](https://mlsanity.com/paper/2410.17518/) (2024)

## Built on by (most cited first, 8 of 8)

- [GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer](https://mlsanity.com/paper/2512.20399/) (2025)
- [Multi-Level Monte Carlo Training of Neural Operators](https://mlsanity.com/paper/2505.12940/) (2025)
- [Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows](https://mlsanity.com/paper/2602.15472/) (2026)
- [Geometric Laplace Neural Operator](https://mlsanity.com/paper/2512.16409/) (2025)
- [GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domains](https://mlsanity.com/paper/2605.03497/) (2026)
- [LEIA: Learned Environment for Interactive Architected Materials](https://mlsanity.com/paper/2605.28368/) (2026)
- [FLARE++: Low-rank attention with dynamic attention routing](https://mlsanity.com/paper/2608.11519/) (2026)
- [CANTO: CAD-Native Transformer Operators for AI-Aided Engineering](https://mlsanity.com/paper/2609.36806/) (2026)

## 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.