PACE-FNO: Physics-Aligned Canonical Equivariance for Fourier Neural Operators

arXiv:2605.18606 · cs.LG · Submitted 2026-05-18 · Read on arXiv

cs.LG

Submitted: 2026-05-18

Updated: 2026-09-27

Code: https://github.com/emoixiao/PACE-FNO

Terminology

• Alignment — 34× in this paper · explained in 1 episode
• Generalization — 21× in this paper · explained in 13 episodes
• Fourier Neural Operator — 11× in this paper
• Adaptation — 10× in this paper · explained in 1 episode
• Adam — 7× in this paper · explained in 2 episodes
• Ablation — 6× in this paper · explained in 1 episode
• Accuracy — 6× in this paper · explained in 1 episode
• Data Augmentation — 6× in this paper · explained in 7 episodes
• Consistency — 5× in this paper · explained in 3 episodes
• Self-consistency — 4× in this paper · explained in 2 episodes
• Distribution Shift — 3× in this paper · explained in 5 episodes
• Error Decomposition — 3× in this paper · explained in 3 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Geometric Mismatch — 2× in this paper · explained in 2 episodes
• Gradient Flow — 2× in this paper · explained in 2 episodes
• Ablation study — 1× in this paper · explained in 1 episode
• Anchor Loss — 1× in this paper · explained in 1 episode
• Catastrophic Forgetting — 1× in this paper · explained in 5 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• DeepONet — 1× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Iterative Refinement — 1× in this paper · explained in 3 episodes
• Latent Representation — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Provenance — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators
• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
• Equivariant Frames and the Impossibility of Continuous Canonicalization
• Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
• Explorations in Homeomorphic Variational Auto-Encoding

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