受拓扑启发的风场超分辨率微调
Topology-Inspired Fine-Tuning for Wind-Field Super-Resolution
AI总结：
该研究针对风场超分辨率，提出用受拓扑启发的辅助损失结合固定对监督微调预训练CNN，在PD和MT距离上实现联合改进，获得1.30 dB PSNR增益。
摘要：
科学超分辨率（SR）模型通常采用逐点重建损失进行优化，但科学解释往往依赖极值、连通区域和多尺度标量结构。我们通过预训练的CNN和GAN风场SR模型来表征这种矛盾。逐点指标、瓶颈持久态图（PD）距离和合并树（MT）距离更青睐CNN，而二阶Wasserstein PD距离则更青睐更清晰的GAN，因此同一拓扑描述符上的不同距离会奖励不同的属性。受这种分歧的启发，我们使用可微的受拓扑启发的辅助损失（针对标量速度、梯度幅度、软高速水平集和局部最大值）以及固定对监督来微调预训练的CNN，固定对监督会约束预测值和持久态，这些持久态位于通过拓扑工具包（Topology ToolKit）离线获取的真实持久态对端点处。我们对16种微调配置进行了损失研究，每种配置都与仅使用原始重建损失的匹配标准微调对照进行比较，研究在固定的168个场基准上进行（每个场的拓扑在固定的160×160子区域上评估）。结果显示，在标量场损失中，梯度监督带来最强的PD改进，但未改善平均MT距离；而固定对监督在PD和MT距离上带来最大且最一致的联合改进。最终目标结合了这两种信号。与预训练的CNN相比，它将平均瓶颈、W₂,∞和W₂,2距离分别降低了31%、25%和27%（相对于对照则降低了32-35%，而对照本身会使这三个距离都恶化），在168个场中的150个场上降低了这三个距离，并获得了1.30 dB的PSNR，约为标准微调增益的一半。平均MT距离也有所改善，但仅在那150个场中的91个场上，表明PD和MT捕捉到了互补结构。
英文摘要：
Scientific super-resolution (SR) models are typically optimized with pointwise reconstruction losses, yet scientific interpretation often hinges on extrema, connected regions, and multiscale scalar structure. We characterize this tension with pretrained CNN and GAN wind-field SR models. Pointwise metrics, bottleneck persistence-diagram (PD) distance, and merge-tree (MT) distance favor the CNN, whereas order-2 Wasserstein PD distances favor the sharper GAN, so even different distances on the same topological descriptor reward different properties. Motivated by this disagreement, we fine-tune the pretrained CNN with differentiable topology-inspired auxiliary losses on scalar speed, gradient magnitude, soft high-speed level sets, and local maxima, and with fixed-pair supervision, which constrains predicted values and persistence at ground-truth persistence-pair endpoints located offline with the Topology ToolKit. A loss study of 16 fine-tuning configurations, each compared with a matched standard fine-tuning control that uses only the original reconstruction loss, on a fixed 168-field benchmark (with topology evaluated on a fixed 160 by 160 subregion of each field), shows that, among the scalar-field losses, gradient supervision provides the strongest PD improvement but does not improve mean MT distance, whereas fixed-pair supervision gives the largest and most consistent joint improvement in PD and MT distances. The final objective combines these two signals. Relative to the pretrained CNN, it lowers mean bottleneck, $W_{2,\infty}$, and $W_{2,2}$ distances by 31%, 25%, and 27% (and by 32-35% relative to the control, which on its own worsens all three), lowers all three on 150 of 168 fields, and gains 1.30 dB PSNR, about half the gain of standard fine-tuning. Mean MT distance also improves, but on only 91 of those 150 fields, indicating that PD and MT capture complementary structure.
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