用小波空间流匹配实现多尺度物理模拟，兼顾精度与效率
Wavelet Flow Matching for Multi-Scale Physics Emulation
- 直接在小波层级空间进行最优传输建模，无需预训练编码器
- 在三个混沌流体系统上实现更长时程的稳定预测与谱一致性
- 适合需要高保真物理模拟且追求计算效率的研究者
由偏微分方程控制的多尺度物理系统模拟要求模型在长时间自回归推演中保持稳定并保留细粒度结构。确定性模拟器会产生过度平滑的预测，而生成式方法虽能捕捉细节但成本高昂。隐空间生成模型虽为折中方案，但仍需额外预训练的自编码器。本文提出小波流匹配（WFM），一种新型生成式模拟器，通过在多尺度小波空间中直接执行最优传输，突破了成本与性能之间的权衡。WFM利用U-Net的层级结构，联合预测指定小波表示下的传输速度。在三个具有挑战性的混沌流体动力学系统上，相比当前最先进模型，WFM实现了更优的长期稳定性、精度和谱相干性。结果明确表明，小波空间是一种有效的免训练表示，适用于复杂物理动态的生成式模拟。
原文摘要 · Abstract (English)
Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions, while generative approaches better capture details but are costly. Latent-space generative models have emerged as a compromise but with the additional cost of separately pre-trained autoencoders. We propose Wavelet Flow Matching (WFM), a novel generative emulator that overcomes current trade-offs between cost and skill by performing optimal-transport directly in the multi-scale wavelet space. Rather than learning a latent compression, WFM leverages the hierarchical structure of a U-Net to jointly predict transport velocities of a prescribed wavelet representation. On three challenging systems of chaotic fluid dynamics, WFM achieves superior long-horizon stability, accuracy and spectral coherence compared to state-of-the-art models. Our results clearly position the wavelet space as an effective training-free representation for generative emulation of complex physical dynamics.
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