From Coarse Training to Fine Inference in Neural Operators via Resolution Adaptation

We address this cross-resolution generalization problem using Polyphase Decomposition. Rather than adapting a pretrained neural operator to a finer discretization, we decompose the high-resolution problem into subproblems at the resolution seen during pretraining, apply the pretrained operator to each subproblem, and recombine their predictions at the target resolution. This yields a zero-shot method, Polyphase Inference, that requires no high-resolution training data. When high-resolution examples are available, the decomposition strategy can be learned and complemented with fine-tuning modules, giving Polyphase Fine-Tuning. Across several PDE benchmarks and neural architectures, Polyphase Inference consistently improves cross-resolution performance over direct evaluation on the target resolution. In the low-data setting, Polyphase Fine-Tuning substantially outperforms standard parameter-efficient adaptation methods while using the same or fewer additional parameters. These results suggest that matching the pretrained input resolution can be an effective component of cross-resolution transfer.