Topology-Inspired Fine-Tuning for Wind-Field Super-Resolution

Key points

• We characterize this tension with pretrained CNN and GAN wind-field SR models.1
• 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.1
• 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.1
• 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.1

Sources (1)

• [1]Topology-Inspired Fine-Tuning for Wind-Field Super-Resolution
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 05:28 PM

  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.

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