Polygonal Domain

Polygonal domains are a focus of research across diverse scientific fields, primarily concerning the efficient and accurate solution of partial differential equations (PDEs) within these irregularly shaped regions. Current research emphasizes developing and analyzing neural network architectures, including deep operator networks and physics-informed neural networks, to solve PDEs on polygonal domains, often leveraging techniques from finite element methods and reinforcement learning to optimize computational efficiency and accuracy. These advancements are significant for applications ranging from additive manufacturing (optimizing laser powder bed fusion processes) to autonomous vehicle navigation (efficient collision avoidance) and material science (modeling nanoscale material properties).