Wavelet Flow Matching for Multi-Scale Physics Emulation

TL;DR

Wavelet Flow Matching (WFM) is a new generative emulation method that operates directly in multi-scale wavelet space, offering improved stability and accuracy for complex physical systems over long predictions.

Contribution

WFM introduces a novel approach that performs optimal transport in wavelet space, avoiding autoencoder pre-training and enhancing multi-scale physical system emulation.

Findings

WFM outperforms state-of-the-art models in stability and accuracy.

WFM maintains spectral coherence over long horizons.

WFM effectively captures fine-scale structures in chaotic fluid dynamics.

Abstract

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.