ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries
arXiv:2608.08608
2026
Architecture
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper's transferable contribution is a deterministic ambient-domain representation that lets one spectral operator handle samples defined on different physical geometries and discretizations. Each geometry is encoded by a signed-distance field on a fixed bounding box, while data and outputs are extended and interpolated to a common rectilinear latent grid; geometry handling is therefore separated from learned Fourier layers. This suggests a practical geometry-conditioned FNO or CNN-like operator with no mesh-specific parameters, point-cloud encoder, or deformation network. The strongest initial test is whether this canonicalization improves cross-geometry generalization and permits zero-shot inference onto target meshes with different resolutions.
Ideas from this paper
✗ Mechanism failed
2026
Embed every variable-domain sample into one fixed ambient hyperrectangle and append its signed-distance function as an additional channel to the operator input. Deterministically extend fields outside the physical domain, resample them onto a shared latent grid, apply standard Fourier layers, then interpolate and mask the output on the requested target discretization. The network learns the operator rather than a separate geometry encoder, so the same weights can be used across shapes and mesh…
Useful7/10
Difficulty4/10
Novelty6/10