We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly incorporate differential equation information into the solution process. This modularity enhances parameter correspondence control, making HAMLET adaptable to PDEs of arbitrary geometries and varied input formats. Notably, HAMLET scales effectively with increasing data complexity and noise, showcasing its robustness. HAMLET is not just tailored to a single type of physical simulation, but can be applied across various domains. Moreover, it boosts model resilience and performance, especially in scenarios with limited data. We demonstrate, through extensive experiments, that our framework is capable of outperforming current techniques for PDEs.

翻译：我们提出了一种新颖的图Transformer框架HAMLET，旨在解决使用神经网络求解偏微分方程（PDEs）所面临的挑战。该框架采用配备模块化输入编码器的图Transformer，将微分方程信息直接整合到求解过程中。这种模块化设计增强了对参数对应关系的控制，使HAMLET能够适应任意几何形状和多样化输入格式的偏微分方程。值得注意的是，HAMLET能够随着数据复杂性和噪声的增加而有效扩展，展现了其鲁棒性。HAMLET不仅适用于单一类型的物理模拟，还可应用于多个领域。此外，它显著提升了模型的鲁棒性和性能，特别是在数据有限的场景下。我们通过大量实验证明，该框架在求解偏微分方程方面能够超越现有技术。