D'Agnese DIF-FNO: Diffeomorphic Implicit Fourier Neural Operators with Topological Guarantees on Non-Convex Domains

Official implementation of D'Agnese DIF-FNO. Introduces the D'Agnese Topological Barrier Loss ($\mathcal{L}_{\text{barrier}}$), a logarithmic barrier potential penalizing Jacobian degeneration to enforce global $C^1$-diffeomorphic invertibility. Guarantees a 0.00% grid folding rate across non-convex geometries (Star, L-Shape, Annulus) while outperforming Geo-FNO and Masked-FNO in relative $L^2$ and Sobolev $H^1$ errors.Official repository: https://github.com/GiovanniDagnese-paper/DIF-FNO.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-26
DOI
https://doi.org/10.5281/zenodo.22117043
Primary Topic
Model Reduction and Neural Networks
Type
preprint
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preprint

D'Agnese DIF-FNO: Diffeomorphic Implicit Fourier Neural Operators with Topological Guarantees on Non-Convex Domains

GIOVANNI D'AGNESE
Zenodo (CERN European Organization for Nuclear Research)
Model Reduction and Neural Networks
preprint

D'Agnese DIF-FNO: Diffeomorphic Implicit Fourier Neural Operators with Topological Guarantees on Non-Convex Domains

GIOVANNI D'AGNESE
preprint en

Abstract

Official implementation of D'Agnese DIF-FNO. Introduces the D'Agnese Topological Barrier Loss ($\mathcal{L}_{\text{barrier}}$), a logarithmic barrier potential penalizing Jacobian degeneration to enforce global $C^1$-diffeomorphic invertibility. Guarantees a 0.00% grid folding rate across non-convex geometries (Star, L-Shape, Annulus) while outperforming Geo-FNO and Masked-FNO in relative $L^2$ and Sobolev $H^1$ errors.Official repository: https://github.com/GiovanniDagnese-paper/DIF-FNO.

Zenodo (CERN European Organization for Nuclear Research)
Model Reduction and Neural Networks
DOIOpen Access PDFOpenAlex
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D'Agnese DIF-FNO: Diffeomorphic Implicit Fourier Neural Operators with Topological Guarantees on Non-Convex Domains — GIOVANNI D'AGNESE · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS