Wavelet Flow Matching for Multi-Scale Physics Emulation

2026-05-15

AI Summary

This work addresses the challenge of simulating multiscale physical systems, which demands both long-term stability and fidelity to fine-scale structures—a balance unmet by existing approaches that are either overly smooth (deterministic models) or computationally prohibitive (generative methods). The authors propose Wavelet Flow Matching (WFM), a novel framework that uniquely integrates optimal transport with multiscale wavelet representations. WFM directly models the transport dynamics in wavelet space without requiring pretrained encoders and leverages a U-Net architecture to jointly predict the evolution velocities of wavelet coefficients across scales. Evaluated on three chaotic fluid systems, WFM significantly outperforms current methods, achieving superior long-term prediction stability, enhanced spatial accuracy, and improved spectral consistency—thereby enabling efficient, high-fidelity generative simulation of complex physical 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.

Problem

• multi-scale physics emulation
• PDEs
• long-horizon stability
• fine-scale structures
• generative modeling

Innovation

• Wavelet Flow Matching
• multi-scale physics emulation
• optimal transport
• generative modeling
• wavelet representation