Wavelet Flow Matching for Multi-Scale Physics Emulation
For researchers needing generative emulators of multi-scale PDEs, WFM overcomes the trade-off between cost and skill by using a training-free wavelet representation, enabling stable long rollouts with preserved fine-scale structures.
Wavelet Flow Matching (WFM) achieves superior long-horizon stability, accuracy, and spectral coherence on three chaotic fluid dynamics systems compared to state-of-the-art models, by performing optimal transport directly in the multi-scale wavelet space without requiring a pre-trained autoencoder.
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.