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. 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.
Abstract (translated)
零样本超分辨率时空预测要求深度学习模型在低分辨率数据上进行训练，并部署到高分辨率数据上进行推理。现有的研究认为，在不同分辨率下保持相似的误差是多分辨率泛化成功的标志。然而，作为数值求解器替代方案的深度学习模型应该随着分辨率的提高而减少误差。基本限制在于，低分辨率数据所能表示的物理定律频率上限由其奈奎斯特频率决定，这使得模型难以处理在高分辨率推理中出现的新频谱成分信号。这导致了错误被锚定在低分辨率上，并被误认为是成功的泛化。我们定义这一根本现象为一个新的问题，即尺度锁定（Scale Anchoring）。 因此，我们提出了一种架构无关的频率表示学习（Frequency Representation Learning, FRL）。通过使用与分辨率对齐的频率表示和谱一致性训练，在具有更高奈奎斯特频率的网格上，FRL增强模型在高频带中的频率响应更为稳定。这使得误差随着分辨率提高而减少，并且在我们设定的任务和分辨率范围内大幅超越基线性能，同时仅带来适度的计算开销。
URL
https://arxiv.org/abs/2512.05132
