The False Promise of Zero-Shot Super-Resolution in Machine-Learned Operators
This addresses a core challenge in scientific machine learning for researchers and practitioners by showing that architectural innovations alone are insufficient for multi-resolution inference, with incremental improvements through a new training method.
The paper tackled the problem of whether machine-learned operators (MLOs) can perform zero-shot super-resolution, finding that they fail to accurately infer at resolutions different from training due to brittleness and aliasing, and proposed a multi-resolution training protocol to address this.
A core challenge in scientific machine learning, and scientific computing more generally, is modeling continuous phenomena which (in practice) are represented discretely. Machine-learned operators (MLOs) have been introduced as a means to achieve this modeling goal, as this class of architecture can perform inference at arbitrary resolution. In this work, we evaluate whether this architectural innovation is sufficient to perform "zero-shot super-resolution," namely to enable a model to serve inference on higher-resolution data than that on which it was originally trained. We comprehensively evaluate both zero-shot sub-resolution and super-resolution (i.e., multi-resolution) inference in MLOs. We decouple multi-resolution inference into two key behaviors: 1) extrapolation to varying frequency information; and 2) interpolating across varying resolutions. We empirically demonstrate that MLOs fail to do both of these tasks in a zero-shot manner. Consequently, we find MLOs are not able to perform accurate inference at resolutions different from those on which they were trained, and instead they are brittle and susceptible to aliasing. To address these failure modes, we propose a simple, computationally-efficient, and data-driven multi-resolution training protocol that overcomes aliasing and that provides robust multi-resolution generalization.