Fine-tuning improves wind-field models using topology-based losses
Topology-Inspired Fine-Tuning for Wind-Field Super-Resolution
Machine Learning
Summary
Wind-field super-resolution models normally focus on precise point-by-point accuracy, but real understanding often depends on large-scale features like connected regions and key points. The authors found that different topological measures can reward different model behaviors, creating a conflict in evaluation. They improved a pretrained CNN model by adding special losses inspired by topology that focus on features like speed gradients and local maxima. This method consistently improved the model’s performance on topological metrics alongside traditional accuracy measures.
What this means in practice
- •For weather modelers: Improve the accuracy of fine-scale wind simulations by incorporating topological constraints during model fine-tuning.
- •For remote sensing engineers: Enhance reconstruction quality of wind fields from low-resolution satellite data using topology-inspired fine-tuning methods.
Authors
Arjun Dadhwal, Brian Summa
Abstract
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.