A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries (2010.09469v2)

Abstract: We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural network based on the PointNet architecture, which learns an end-to-end mapping between spatial positions and CFD quantities. Using our approach, (i) the network inherits desirable features of unstructured meshes (e.g., fine and coarse point spacing near the object surface and in the far field, respectively), which minimizes network training cost; (ii) object geometry is accurately represented through vertices located on object boundaries, which maintains boundary smoothness and allows the network to detect small changes between geometries; and (iii) no data interpolation is utilized for creating training data; thus accuracy of the CFD data is preserved. None of these features are achievable by extant methods based on projecting scattered CFD data into Cartesian grids and then using regular convolutional neural networks. Incompressible laminar steady flow past a cylinder with various shapes for its cross section is considered. The mass and momentum of predicted fields are conserved. We test the generalizability of our network by predicting the flow around multiple objects as well as an airfoil, even though only single objects and no airfoils are observed during training. The network predicts the flow fields hundreds of times faster than our conventional CFD solver, while maintaining excellent to reasonable accuracy.

• The paper presents a novel deep learning framework adapting PointNet to predict fluid flow fields using point clouds from unstructured CFD grids.
• This method avoids data interpolation, preserves mesh features and geometric fidelity, and efficiently handles irregular geometries without artificial roughness.
• Numerical results show the framework achieves hundreds of times speedup over traditional CFD solvers while maintaining high accuracy and generalization on complex shapes.

Overview of "A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries"

The paper, "A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries," presents an innovative approach for predicting fluid flow fields using a deep learning framework specifically designed for domains with irregular geometries. This methodology leverages unstructured grids within computational fluid dynamics (CFD) domains by treating grid vertices as point clouds, integrating them into a neural network architecture rooted in PointNet, which facilitates an efficient end-to-end mapping from spatial positions to CFD quantities.

Key Contributions and Methodology

The primary contribution of this research lies in its novel adaptation of PointNet architecture for fluid dynamics applications. By representing CFD grid vertices as point clouds, the proposed model efficiently learns flow field dynamics without necessitating the interpolation of CFD data into Cartesian grids, which conventional CNN-based approaches typically require. This framework demonstrates several advantages, notably:

1. Preservation of Unstructured Mesh Features: By using the inherent characteristics of unstructured meshes, the model optimizes training cost through variable point spacing, which is denser near object surfaces where high resolution is needed.
2. Geometric Fidelity: Point clouds accurately encode object geometry at boundary vertices, maintaining surface smoothness and allowing for high sensitivity to subtle geometrical changes. This advantage mitigates issues of artificial surface roughness introduced by voxel-based methods.
3. Elimination of Data Interpolation: Directly utilizing CFD data without interpolation preserves numerical accuracy, addressing one of the critical limitations of existing deep learning frameworks for flow prediction.

The authors test their framework on incompressible laminar steady flow past a cylinder with various cross-sectional shapes. The model is validated not only on single objects but also on composite geometries and an airfoil, which it successfully handles despite training on simpler geometries.

Numerical Results and Analysis

The paper reports that the proposed network achieves significant computational speedups—up to several hundred times faster than conventional CFD solvers—while maintaining excellent predictive accuracy. This improvement is critical given the traditionally high computational demands of CFD simulations, specifically when exploring complex geometrical configurations. The accuracy of the predicted flow fields is quantitatively assessed using pointwise error metrics and the conservation properties of mass and momentum, where results exhibit promising generalization capabilities.

Implications and Future Directions

From a practical standpoint, the ability to rapidly and accurately predict fluid flows over complex and dynamic geometries has substantial implications across multiple fields, including aerospace design and environmental simulations. The paper highlights a robust approach that significantly reduces the computational burden associated with CFD simulations without compromising precision, offering a compelling alternative for scenarios where rapid model evaluations are necessary.

Theoretically, the methodology introduces a paradigm shift in the representation of fluid dynamics problems within deep learning frameworks. By bypassing the need for traditional grid mappings, the point-cloud approach aligns more naturally with the intrinsic structure of CFD data, potentially opening pathways for more intricate fluid behavior modeling in three and higher-dimensional spaces.

Future research directions pointed out by the authors include extending the framework to handle unsteady flows, leveraging more complex neural architectures such as PointNet++ for improved generalizability, and integrating this approach with physics-informed neural networks (PINNs) to exploit governing equations directly within the learning algorithm. Additionally, further exploration of this method in turbulent flow regimes could enhance its applicability to a wider array of fluid dynamics challenges.