HAMLET: Graph Transformer Neural Operator for Partial Differential
  Equations
Andrey Bryutkin Jiahao Huang Zhongying Deng Guang Yang Carola-Bibiane Schönlieb Angelica Aviles-Rivero
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.