Learning Temporally Consistent Turbulence Between Sparse Snapshots via Diffusion Models

TL;DR

This paper introduces a diffusion model-based method to generate temporally consistent turbulent flow sequences between sparse snapshots, effectively capturing complex turbulent dynamics in 2D and 3D flows.

Contribution

The paper presents a novel application of conditional diffusion models as a surrogate for reconstructing turbulent flow sequences from sparse data, demonstrating statistical and physical accuracy.

Findings

Successfully reconstructed turbulent flow sequences with statistical fidelity.

Captured evolving flow statistics in non-stationary turbulence.

Generated physically consistent instantaneous flow fields.

Abstract

We investigate the statistical accuracy of temporally interpolated spatiotemporal flow sequences between sparse, decorrelated snapshots of turbulent flow fields using conditional Denoising Diffusion Probabilistic Models (DDPMs). The developed method is presented as a proof-of-concept generative surrogate for reconstructing coherent turbulent dynamics between sparse snapshots, demonstrated on a 2D Kolmogorov Flow, and a 3D Kelvin-Helmholtz Instability (KHI). We analyse the generated flow sequences through the lens of statistical turbulence, examining the time-averaged turbulent kinetic energy spectra over generated sequences, and temporal decay of turbulent structures. For the non-stationary Kelvin-Helmholtz Instability, we assess the ability of the proposed method to capture evolving flow statistics across the most strongly time-varying flow regime. We additionally examine instantaneous fields and physically motivated metrics at key stages of the KHI flow evolution.