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

2024-06-30

AI Summary

This work addresses geometry-driven flow field prediction by proposing the first conditional diffusion model framework for geometry-to-flow generation. Methodologically, it conditions the diffusion process on obstacle geometry using a U-Net architecture enhanced with cross-attention mechanisms and incorporates a learnable Markov kernel to progressively reconstruct physically consistent instantaneous flow fields from Gaussian noise. The key contribution lies in pioneering the integration of conditional diffusion models into computational fluid dynamics modeling, markedly improving generalization to complex geometries—such as the character “PKU”. Experiments demonstrate superior performance over CNN- and VAE-based baselines in both interpolation and extrapolation tasks. Generated flow fields exhibit lower divergence, enhanced physical plausibility, and improved quantitative accuracy and robustness across diverse geometric configurations.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work

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.

Problem

• Predict flow fields around obstacles using obstacle shapes as input
• Compare diffusion model performance with CNN and VAE models
• Evaluate model robustness on simple and complex obstacle geometries

Innovation

• Geometry-to-flow diffusion model predicts flow fields
• U-Net with cross-attention integrates obstacle geometry
• Superior performance over CNN and VAE models