GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911007710904320 |
|---|---|
| author | Ramezankhani, Milad Patel, Janak M. Deodhar, Anirudh Birru, Dagnachew |
| author_facet | Ramezankhani, Milad Patel, Janak M. Deodhar, Anirudh Birru, Dagnachew |
| contents | We present a novel graph-informed transformer operator (GITO) architecture for learning complex partial differential equation systems defined on irregular geometries and non-uniform meshes. GITO consists of two main modules: a hybrid graph transformer (HGT) and a transformer neural operator (TNO). HGT leverages a graph neural network (GNN) to encode local spatial relationships and a transformer to capture long-range dependencies. A self-attention fusion layer integrates the outputs of the GNN and transformer to enable more expressive feature learning on graph-structured data. TNO module employs linear-complexity cross-attention and self-attention layers to map encoded input functions to predictions at arbitrary query locations, ensuring discretization invariance and enabling zero-shot super-resolution across any mesh. Empirical results on benchmark PDE tasks demonstrate that GITO outperforms existing transformer-based neural operators, paving the way for efficient, mesh-agnostic surrogate solvers in engineering applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Ramezankhani, Milad Patel, Janak M. Deodhar, Anirudh Birru, Dagnachew Machine Learning We present a novel graph-informed transformer operator (GITO) architecture for learning complex partial differential equation systems defined on irregular geometries and non-uniform meshes. GITO consists of two main modules: a hybrid graph transformer (HGT) and a transformer neural operator (TNO). HGT leverages a graph neural network (GNN) to encode local spatial relationships and a transformer to capture long-range dependencies. A self-attention fusion layer integrates the outputs of the GNN and transformer to enable more expressive feature learning on graph-structured data. TNO module employs linear-complexity cross-attention and self-attention layers to map encoded input functions to predictions at arbitrary query locations, ensuring discretization invariance and enabling zero-shot super-resolution across any mesh. Empirical results on benchmark PDE tasks demonstrate that GITO outperforms existing transformer-based neural operators, paving the way for efficient, mesh-agnostic surrogate solvers in engineering applications. |
| title | GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.13906 |