A point-cloud deep learning framework for prediction of fluid flow fields on irregular geometries

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.

Metamodel-based multidisciplinary design optimization methods for aerospace system

“…In addition to the aforementioned data-driven machine learning techniques, physics-informed machine learning techniques, also known as physics-informed neural networks [156,157], have emerged as an alternative to illposed and inverse problems. Fundamental physical laws and domain knowledge are embedded by exploiting observational data [158,159], tailoring neural network architecture for physics constraints [160,161], and/or imposing physics constraints into the loss function [162,163]. The physics-informed neural network is expected to outperform existing machine learning methods in partially understood, uncertain, and high-dimensional problems.…”

Alternative Artificial Neural Network Structures for Turbulent Flow Velocity Field Prediction

“…Each simulation was carried out with one of the geometries shown in Table 1. These geometries are based on the geometries of the study of Kashefi et al [14], and they were generated by changing the size and orientation of eight basic geometries. With the previously mentioned domain, an unstructured polygonal mesh of around 50,000 cells was generated.…”

“…The values of the fields are interpolated in order to fit the data into a 128 × 256 grid. Then, the procedure of Kashefi et al [14] for data generation is followed.…”

“…Ribeiro et al [13] and Kashefi et al [14], using CNN architectures, achieved very accurate results for velocity and pressure fields of stationary fluids around simple shaped obstacles, with a computational cost three to five orders of magnitude lower than CFD simulations. In addition, in the study conducted by Kashefi et al [14], different velocity and pressure fields were obtained with slight modifications of the geometry, which is essential for design optimization.…”

“…Nowruzi et al [15] analysed the behaviour of two airfoils in 2D and 3D using CFD and an ANN, and showed good agreements between the results obtained by both methods. Compared to two-dimensional systems, the main disadvantage of analysing three-dimensional systems using DL is the limited workspace [14]. For this reason, Mohan et al [16] developed a DL-based infrastructure that performs a dimensional reduction of the geometry in order to analyse the flow characteristics susequently.…”