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

Abstract

Zero-Shot Super-Resolution Spatiotemporal Forecasting requires a deep learning model to be trained on low-resolution data and deployed for inference on high-resolution. Existing studies consider **maintaining** similar error across different resolutions as indicative of successful multi-resolution generalization performance. However, deep learning models serving as alternatives to numerical solvers should **reduce** error as resolution increases. The fundamental limitation is, the upper bound of physical law frequencies that low-resolution data can represent is constrained by its Nyquist frequency, making it difficult for models to process signals containing unseen frequency components during high-resolution inference. *This results in errors being anchored at low resolution, incorrectly interpreted as successful generalization.* We define this fundamental phenomenon as a new problem distinct from existing issues: **Scale Anchoring**. Therefore, we propose architecture-agnostic Frequency Representation Learning. It alleviates Scale Anchoring through resolution-aligned frequency representations and spectral consistency training: on grids with higher Nyquist frequencies, the frequency response in high-frequency bands of FRL-enhanced variants is more stable. This allows errors to decrease with resolution and significantly outperform baselines within our task and resolution range, while incurring only modest computational overhead.