Learning Operators of Geometry with an Interface AutoencoderNew

This paper addresses the challenge of learning operators for geometry-dependent PDEs where inputs and outputs consist of oriented interfaces and functions defined on those interfaces. The authors establish an approximation theorem for continuous operators between general state sets and instantiate it with the Interface Autoencoder (IAE), which represents interface-function states in a fixed computational domain using finite projection codes. This approach enables neural operators to handle variable geometries that traditional fixed-domain methods cannot process.