GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations

• URL: http://arxiv.org/abs/2506.13906v1
• Date: Mon, 16 Jun 2025 18:35:45 GMT
• Title: GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations
• Authors: Milad Ramezankhani, Janak M. Patel, Anirudh Deodhar, Dagnachew Birru,
• Abstract summary: We present a novel graph-informed transformer operator (GITO) architecture for learning complex partial differential equation systems.<n>GITO consists of two main modules: a hybrid graph transformer (HGT) and a transformer neural operator (TNO)<n> Empirical results on benchmark PDE tasks demonstrate that GITO outperforms existing transformer-based neural operators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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