Breaking Scale Anchoring: Frequency Representation Learning for Accurate High-Resolution Inference from Low-Resolution Training

Wenshuo Wang, Fan Zhang† († Corresponding Author)

• When deep learning models perform spatiotemporal forecasting at higher resolutions, they do not exhibit the power-law error decay characteristic of numerical solvers. Instead, their accuracy remains almost unchanged. We regard this long-accepted behavior as a problem, which we term Scale Anchoring.
• We identify the core limitation behind Scale Anchoring as the Nyquist frequency of the training data. Based on this insight, we propose Frequency Representation Learning to induce frequency-domain extrapolation with only minor computational overhead, enabling the model to mitigate this issue.

Recommended citation: Wenshuo Wang, Fan Zhang. "Breaking Scale Anchoring: Frequency Representation Learning for Accurate High-Resolution Inference from Low-Resolution Training." preprint, 2025.