ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries
Fourier neural operators (FNOs) provide efficient nonlocal spectral learning, but varying geometries and independently chosen discretizations remain difficult to accommodate. We introduce the ambient-domain extension Fourier neural operator (ADEx-FNO), a deterministic framework that incorporates geometry without modifying the defining Fourier-operator layers. Each physical domain is embedded in a fixed ambient hypercube and represented by a signed distance function. Inputs and solution fields are deterministically extended to the ambient domain, transferred to a common, potentially nonuniform rectilinear latent grid, processed by the FNO, then interpolated to an independently chosen targe...
| Authors | Roberto Nuca, Giovanni Testa, Luca Galimberti et al. |
|---|---|
| Primary category | math.NA |
| Published | 9 August 2026 |
| Last updated at source | 9 August 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.