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Unfolding Time: Generative Modeling for Turbulent Flows in 4D

Abdullah Saydemir, Marten Lienen, Stephan Günnemann

TL;DR

The paper addresses the need for temporally coherent generative surrogates of turbulent flows by extending diffusion-based turbulence modeling to 4D. It develops a 4D diffusion architecture that combines a 3D U-Net with bi-directional ConvGRU to generate sequences of 3D flow states, and introduces physics-informed Navier–Stokes guidance to enforce physical plausibility during sampling. The authors show that the 4D model can produce time-varying simulations with quality comparable to 3D snapshot baselines, while the guidance improves spectral and regional flow statistics. This approach enables efficient exploration of turbulence dynamics and supports temporal analyses such as mixing and evolution of coherent structures in CFD surrogates.

Abstract

A recent study in turbulent flow simulation demonstrated the potential of generative diffusion models for fast 3D surrogate modeling. This approach eliminates the need for specifying initial states or performing lengthy simulations, significantly accelerating the process. While adept at sampling individual frames from the learned manifold of turbulent flow states, the previous model lacks the capability to generate sequences, hindering analysis of dynamic phenomena. This work addresses this limitation by introducing a 4D generative diffusion model and a physics-informed guidance technique that enables the generation of realistic sequences of flow states. Our findings indicate that the proposed method can successfully sample entire subsequences from the turbulent manifold, even though generalizing from individual frames to sequences remains a challenging task. This advancement opens doors for the application of generative modeling in analyzing the temporal evolution of turbulent flows, providing valuable insights into their complex dynamics.

Unfolding Time: Generative Modeling for Turbulent Flows in 4D

TL;DR

The paper addresses the need for temporally coherent generative surrogates of turbulent flows by extending diffusion-based turbulence modeling to 4D. It develops a 4D diffusion architecture that combines a 3D U-Net with bi-directional ConvGRU to generate sequences of 3D flow states, and introduces physics-informed Navier–Stokes guidance to enforce physical plausibility during sampling. The authors show that the 4D model can produce time-varying simulations with quality comparable to 3D snapshot baselines, while the guidance improves spectral and regional flow statistics. This approach enables efficient exploration of turbulence dynamics and supports temporal analyses such as mixing and evolution of coherent structures in CFD surrogates.

Abstract

A recent study in turbulent flow simulation demonstrated the potential of generative diffusion models for fast 3D surrogate modeling. This approach eliminates the need for specifying initial states or performing lengthy simulations, significantly accelerating the process. While adept at sampling individual frames from the learned manifold of turbulent flow states, the previous model lacks the capability to generate sequences, hindering analysis of dynamic phenomena. This work addresses this limitation by introducing a 4D generative diffusion model and a physics-informed guidance technique that enables the generation of realistic sequences of flow states. Our findings indicate that the proposed method can successfully sample entire subsequences from the turbulent manifold, even though generalizing from individual frames to sequences remains a challenging task. This advancement opens doors for the application of generative modeling in analyzing the temporal evolution of turbulent flows, providing valuable insights into their complex dynamics.
Paper Structure (12 sections, 6 equations, 7 figures, 1 table)

This paper contains 12 sections, 6 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Dataset
  4. Generative Turbulence Simulation
  5. Generative Diffusion Models
  6. Method
  7. Physics-inspired Guidance
  8. Experiments
  9. Navier-Stokes Guidance
  10. Limitations & Future Work
  11. Conclusion
  12. Samples from the 4D model

Figures (7)

  • Figure 1: A time-varying 3D turbulent flow simulation generated by our model. Visualization shows the magnitude of the velocity field ${\bm{u}}$. The insets show that the flow evolves coherently at a similar rate as a ground-truth sample of the same region.
  • Figure 2: Architecture of our model for the denoised mean prediction $\mu_{\bm{\theta}}({\bm{x}}_t, t)$ in the DDPM framework. The model synchronizes the denoising process along the time dimension at each down- and up-sampling level of the U-Net with bi-directional ConvGRU layers.
  • Figure 3: A generated sample for the step-high case compared to a ground-truth example. The dotted grid provides visual support to highlight the dynamics of the flow.
  • Figure 4: A generated sample from case wide-elbow. wide-elbow is an "L" shape rotated 90 degrees clockwise.
  • Figure 5: A generated sample from case cross-offset. cross-offset is a cross but the lines intersect each other on the side rather than in the middle.
  • ...and 2 more figures