Flow Matching and Diffusion Models via PointNet for Generating Fluid Fields on Irregular Geometries

TL;DR

This paper introduces two new deep learning frameworks, Flow Matching PointNet and Diffusion PointNet, for accurately predicting fluid flow on irregular geometries using point-cloud data, avoiding pixelation and high-frequency noise artifacts.

Contribution

The paper proposes novel PointNet-based flow matching and diffusion models that operate directly on point clouds, providing more accurate and robust fluid flow predictions on irregular geometries.

Findings

Achieve more accurate velocity and pressure predictions.

Demonstrate robustness to incomplete geometries.

Avoid high-frequency noise artifacts in predicted fields.

Abstract

We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion models, respectively. In these frameworks, a reverse generative process reconstructs physical fields from standard Gaussian noise conditioned on unseen geometries. The proposed approaches operate directly on point-cloud representations of computational domains (e.g., grid vertices of finite-volume meshes) and therefore avoid the limitations of pixelation used to project geometries onto uniform lattices, as is common in U-Net-based flow matching and diffusion models. In contrast to graph neural network-based diffusion models, Flow Matching PointNet and Diffusion PointNet do not exhibit high-frequency noise artifacts in the predicted fields. Moreover, unlike such approaches, which require auxiliary intermediate networks to condition geometry, the proposed frameworks rely solely on PointNet, resulting in a simple and unified architecture. The performance of the proposed frameworks is evaluated on steady incompressible flow past a cylinder, using a geometric dataset constructed by varying the cylinder's cross-sectional shape and orientation across samples. The results demonstrate that Flow Matching PointNet and Diffusion PointNet achieve more accurate predictions of velocity and pressure fields, as well as lift and drag forces, and exhibit greater robustness to incomplete geometries compared to a vanilla PointNet with the same number of trainable parameters.