Generative prediction of flow fields around an obstacle using the diffusion model

TL;DR

This paper introduces a diffusion model conditioned on obstacle shape to accurately predict flow fields around various geometries, outperforming CNN and VAE models in complex scenarios.

Contribution

The paper presents a novel geometry-to-flow diffusion model that effectively incorporates obstacle shape via cross-attention, improving flow prediction accuracy and generalization.

Findings

Outperforms CNN and VAE models in flow prediction accuracy.

Demonstrates robustness in complex and unseen geometries.

Effective interpolation and generalization across obstacle shapes.

Abstract

We propose a geometry-to-flow diffusion model that utilizes obstacle shape as input to predict a flow field around an obstacle. The model is based on a learnable Markov transition kernel to recover the data distribution from the Gaussian distribution. The Markov process is conditioned on the obstacle geometry, estimating the noise to be removed at each step, implemented via a U-Net. A cross-attention mechanism incorporates the geometry as a prompt. We train the geometry-to-flow diffusion model using a dataset of flows around simple obstacles, including circles, ellipses, rectangles, and triangles. For comparison, two CNN-based models and a VAE model are trained on the same dataset. Tests are carried out on flows around obstacles with simple and complex geometries, representing interpolation and generalization on the geometry condition, respectively. To evaluate performance under demanding conditions, the test set incorporates scenarios including crosses and the characters `PKU.' Generated flow fields show that the geometry-to-flow diffusion model is superior to the CNN-based models and the VAE model in predicting instantaneous flow fields and handling complex geometries. Quantitative analysis of the accuracy and divergence demonstrates the model's robustness.