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Denoising diffusion and latent diffusion models for physics field simulations

Yuan Jia, Chi Zhang, Hao Ma, Qiao Zhang, Kai Liu, Chih-Yung Wen

Abstract

Accurate prediction of physical fields is critical in various engineering applications, including thermal management in electronic systems, airfoil shape optimization in aerospace, and flow field control in hypersonic vehicles. This study employs the Denoising Diffusion Probabilistic Models (DDPMs) for predicting the temperature field caused by the thermal diffusion, and the flow fields spanning from incompressible to hypersonic regimes. A conditional DDPM framework is first validated with a steady-state thermal diffusion problem by predicting the temperature distribution around a plate with holes. Strong agreement with ground truth data is shown with an average error of approximately 0.013 for plates with a central circular hole. The model also delivers high accuracy in critical regions, such as near the inner circular or square holes. Its performance is further evaluated on incompressible flow around an airfoil and hypersonic flow over a compression ramp, confirming robust predictive capability across diverse flow conditions. Additionally, a latent-space implementation of DDPM is introduced, which employs an Autoencoder (AE) for dimensionality reduction and reconstruction of the physical data. The resulting Latent Diffusion Model (LDM) maintains reconstruction quality comparable to the standard DDPM while substantially reducing the computational cost of the diffusion training process. When applied to hypersonic flow over a compression ramp in the original parameter space, LDM predictions align well with ground truth, achieving a deviation of only 4.28% in separation length estimation. This work confirms the high predictive accuracy of the DDPM framework and highlights the efficiency gains from performing diffusion in a learned latent space. The findings establish an efficient framework for high fidelity generative modeling of complex thermal/flow fields.

Denoising diffusion and latent diffusion models for physics field simulations

Abstract

Accurate prediction of physical fields is critical in various engineering applications, including thermal management in electronic systems, airfoil shape optimization in aerospace, and flow field control in hypersonic vehicles. This study employs the Denoising Diffusion Probabilistic Models (DDPMs) for predicting the temperature field caused by the thermal diffusion, and the flow fields spanning from incompressible to hypersonic regimes. A conditional DDPM framework is first validated with a steady-state thermal diffusion problem by predicting the temperature distribution around a plate with holes. Strong agreement with ground truth data is shown with an average error of approximately 0.013 for plates with a central circular hole. The model also delivers high accuracy in critical regions, such as near the inner circular or square holes. Its performance is further evaluated on incompressible flow around an airfoil and hypersonic flow over a compression ramp, confirming robust predictive capability across diverse flow conditions. Additionally, a latent-space implementation of DDPM is introduced, which employs an Autoencoder (AE) for dimensionality reduction and reconstruction of the physical data. The resulting Latent Diffusion Model (LDM) maintains reconstruction quality comparable to the standard DDPM while substantially reducing the computational cost of the diffusion training process. When applied to hypersonic flow over a compression ramp in the original parameter space, LDM predictions align well with ground truth, achieving a deviation of only 4.28% in separation length estimation. This work confirms the high predictive accuracy of the DDPM framework and highlights the efficiency gains from performing diffusion in a learned latent space. The findings establish an efficient framework for high fidelity generative modeling of complex thermal/flow fields.
Paper Structure (15 sections, 19 equations, 25 figures, 5 tables)

This paper contains 15 sections, 19 equations, 25 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Denoising Diffusion Probabilistic Model (DDPM)
  4. Latent Diffusion Model (LDM)
  5. Evaluation Metrics
  6. Experimental cases
  7. Plate temperature distributions
  8. Incompressible airfoil flow fields
  9. Hypersonic flow over compression ramp
  10. Results and analysis
  11. Predictions of plate temperature distribution
  12. Predictions of airfoil flow fields
  13. Predictions of hypersonic flow fields
  14. Predictions of full hypersonic flow fields by LDM
  15. Conclusion

Figures (25)

  • Figure 1: The architecture of the Denoising Diffusion Probabilistic Model (DDPM).
  • Figure 2: Details of the DDPM. (a): The network structure; Dashed lines represent skip connections; Bold dash lines denote that not all layers are displayed; (b): Detail of each block.
  • Figure 3: The architecture of the Latent Diffusion Model (LDM) with details of each block.
  • Figure 4: The schematic diagram for plates with holes. (a)-(e) represent 5 boundary conditions, blue corresponds to a temperature of 0, green to 0.5, and red to 1.
  • Figure 5: The hypersonic flow structure over a compression ramp with computational domain in red lines.
  • ...and 20 more figures