GITO用图结构增强Transformer，高效求解不规则网格上的复杂微分方程。
GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations
- 融合图神经网络与Transformer，捕捉局部与长程空间关系。
- 在多个基准PDE任务上超越现有方法，支持零样本超分辨率。
- 适合需要高精度、网格无关的工程仿真建模场景。
我们提出一种新型图结构感知的Transformer算子（GITO），用于学习定义在不规则几何和非均匀网格上的复杂偏微分方程系统。GITO由混合图Transformer（HGT）和Transformer神经算子（TNO）两部分组成。HGT结合图神经网络（GNN）编码局部空间关系，利用Transformer捕捉长程依赖，并通过自注意力融合层整合两者输出，提升图结构数据的特征表达能力。TNO模块采用线性复杂度的交叉注意力与自注意力机制，将编码后的输入函数映射到任意查询位置的预测结果，实现对离散化的不变性，并支持跨任意网格的零样本超分辨率。在多个基准PDE任务上的实验表明，GITO优于现有的基于Transformer的神经算子，为工程应用中的高效、网格无关代理求解器开辟了新路径。
原文摘要 · Abstract (English)
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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