HAMLET: Graph Transformer Neural Operator for Partial Differential Equations

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 …

challenges control cs.lg cs.na differential differential equation equation framework graph information making math.na modular networks neural networks novel process solution transformer transformers