ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries

This paper presents ADEx-FNO (Ambient-Domain Extension Fourier Neural Operator), a deterministic framework enabling Fourier neural operators to handle varying geometries and independently chosen discretizations without modifying the defining spectral layers. The method embeds each physical domain into a fixed ambient hypercube and represents boundaries via signed distance functions, allowing seamless handling of diverse computational meshes while maintaining FNO's computational efficiency.