GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations
This work addresses the challenge of developing efficient surrogate solvers for PDEs in engineering applications, representing an incremental improvement over existing transformer-based methods.
The paper tackled the problem of learning complex partial differential equations on irregular geometries and non-uniform meshes by introducing the GITO architecture, which outperformed existing transformer-based neural operators on benchmark tasks, paving the way for efficient, mesh-agnostic surrogate solvers.
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.