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From Zero to Turbulence: Generative Modeling for 3D Flow Simulation

ICLR 2024 · Probabilistic and scientific modeling › Molecules and proteins · approach: Flow matching generative modeling · 7 citations (OpenAlex)

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Proposes TurbDiff, a 3D DDPM-based generative model that samples turbulent flow states from scratch given domain geometry and boundary conditions, without initial states or long autoregressive roll-outs, evaluated on a new 3D turbulence dataset with two new distribution metrics.

Problem

Autoregressive surrogate models for 3D turbulent flow need very small time steps and long roll-outs with error accumulation, or a realistic initial state from a numerical solver, limiting their usefulness as replacements for CFD solvers.

Approach

Treat turbulent flow simulation as generative sampling of the marginal distribution of turbulent flow states conditioned on geometry/boundary conditions, using a 3D U-Net DDPM with transformer bottleneck and boundary-conditioned (Dirichlet-style inpainting) sampling of fixed cells, plus two new sample metrics (TKE-spectrum W2 and region-wise velocity/vorticity/pressure W2).

Key results

• TurbDiff achieves W2,TKE 3.9±0.4 and W2,R 1.38±0.04, close to DilResNet-22 (2.15 and 1.240) which requires a true initial state.
• TurbDiff generates a sample in about 20.63 s versus roughly 10 minutes of solver time for the initial transition, a claimed ~30x speedup over the numerical solver.
• Autoregressive baselines rolled out from noise-perturbed initial states (-init) suffer severe error accumulation, e.g. DilResNet-init W2,R of 4.6e8.

Measured effects reported in the paper

Surprising findings

• Euclidean distance is a poor sample metric for turbulence because the smooth mean flow is closer to all samples than uncorrelated turbulent samples are to each other.

Limitations

• Cubic scaling of 3D grid representation with resolution; diffusion sampling is expensive.
• Grid embedding approximates geometry only at 0th order (step functions), hurting sharp-corner or smooth geometries.
• No exploited physical symmetries (translation, rotation, reflection equivariance, Reynolds similarity).

Experimental setup

Datasets: OpenFOAM LES turbulent channel-flow simulations with 45 objects

Benchmarks: 3D turbulence dataset (9 unseen test simulations)

Metrics: W2 TKE spectrum distance W2 region-based distributional distance RMSE of max-TKE location runtime

Baselines: TF-Net-init TF-Net-22 DilResNet-init DilResNet-22

Builds on: DDPM U-Net inpainting with diffusion models DilResNet TF-Net

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