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

TL;DR

GITO introduces a graph-informed transformer architecture that effectively learns complex PDE systems on irregular geometries, combining local and global features for improved accuracy and mesh-agnostic predictions.

Contribution

The paper proposes a novel GITO architecture integrating GNNs and transformers, enabling discretization-invariant PDE learning on irregular meshes with superior performance.

Findings

Outperforms existing transformer-based neural operators on benchmark PDE tasks.

Enables zero-shot super-resolution across arbitrary meshes.

Provides a mesh-agnostic surrogate solver for complex PDEs.

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.