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

arXiv:2608.08608 · math.NA, cs.CE, cs.LG, cs.NA · Submitted 2026-08-09 · Read on arXiv

Roberto Nuca, Giovanni Testa, Luca Galimberti, Matteo Parsani

math.NA, cs.CE, cs.LG, cs.NA

Submitted: 2026-08-09

Updated: 2026-08-11

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Fourier Neural Operator — 15× in this paper
• Signed Distance Function — 12× in this paper
• Accuracy — 11× in this paper · explained in 1 episode
• Consistency — 10× in this paper · explained in 3 episodes
• Neural Operators — 7× in this paper · explained in 2 episodes
• DeepONet — 5× in this paper · explained in 2 episodes
• Fidelity — 5× in this paper · explained in 2 episodes
• Latent Representation — 5× in this paper · explained in 2 episodes
• Benchmark — 4× in this paper · explained in 2 episodes
• Computational Efficiency — 4× in this paper · explained in 2 episodes
• Point Clouds — 4× in this paper · explained in 2 episodes
• Robustness — 4× in this paper · explained in 6 episodes
• Transformer — 4× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 14 episodes
• Uncertainty Quantification — 3× in this paper · explained in 9 episodes
• Fast Fourier Transform — 2× in this paper
• Fourier Neural Operator (FNO) — 2× in this paper · explained in 3 episodes
• Inverse Problem — 2× in this paper · explained in 2 episodes
• King Abdullah University of Science and Technology — 2× in this paper
• Preconditioner — 2× in this paper · explained in 2 episodes
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalization Capabilities — 1× in this paper · explained in 2 episodes
• Geometric Distribution — 1× in this paper · explained in 2 episodes
• Hyperparameters — 1× in this paper · explained in 2 episodes
• MeanFlow — 1× in this paper · explained in 2 episodes
• Nonuniform Discrete Fourier Transform — 1× in this paper
• Signed Distance Function (SDF) — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes
• Weight Decay — 1× in this paper · explained in 2 episodes

Sources

• A Library for Learning Neural Operators

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