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.

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

We propose a customized convolutional neural network based autoencoder called a hierarchical autoencoder, which allows us to extract nonlinear autoencoder modes of flow fields while preserving the contribution order of the latent vectors. As preliminary tests, the proposed method is first applied to a cylinder wake at $Re_D$ = 100 and its transient process. It is found that the proposed method can extract the features of these laminar flow fields as the latent vectors while keeping the order of their energy content. The present hierarchical autoencoder is further assessed with a two-dimensional $y-z$ cross-sectional velocity field of turbulent channel flow at $Re_{\tau}$ = 180 in order to examine its applicability to turbulent flows. It is demonstrated that the turbulent flow field can be efficiently mapped into the latent space by utilizing the hierarchical model with a concept of ordered autoencoder mode family. The present results suggest that the proposed concept can be extended to meet various demands in fluid dynamics including reduced order modeling and its combination with linear theory-based methods by using its ability to arrange the order of the extracted nonlinear modes.

Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data

CNN-LSTM based reduced order modeling of two-dimensional unsteady flows around a circular cylinder at different Reynolds numbers

Data-driven modeling for unsteady aerodynamics and aeroelasticity

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.

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

A novel spatial-temporal prediction method for unsteady wake flows based on hybrid deep neural network

A general and flexible approximation model based on convolutional neural network (ConvNet) technique as well as a signed distance function (SDF) is proposed to predict aerodynamic coefficients of the airfoils in this paper. Traditional surrogate-based prediction methods are blamed for its limited dimensions of design variables and powerless for strong nonlinear engineering problems. Considering that ConvNets have been proven to be suitable for nonlinear and high-dimensional practical tasks in complex image identification and speech recognition, a two-layer ConvNet framework rather than conventional Kriging surrogate model is built to predict aerodynamic coefficients for large-scale nonlinear problems. In order to build the bridge between geometry information and the ConvNet, a new geometry representation method based on SDF is also applied. Furthermore, numerical studies are presented for wind turbine airfoils at a high angle of attack. Compared to ordinary Kriging model, the ConvNet-based method exhibits competitive prediction accuracy within the certain error margin. Moreover, the influence of the ConvNet’s nonlinear activation functions on the predictive effect is studied in both training and validation datasets.

Aerodynamic Coefficient Prediction of Airfoils with Convolutional Neural Network

Fluid-structure interaction analysis has high computing costs when using computational fluid dynamics. These costs become prohibitive when optimizing the fluid-structure interaction system, because of the huge sample space of structural parameters. To overcome this realistic challenge, a deep neural network based reduced-order model for fluid-structure interaction system is developed to quickly and accurately predict the flow field in fluid-structure interaction system. This deep neural network can predict the flow field at the next time step based on the current flow field and the structural motion conditions. A fluid-structure interaction model can be constructed by combining the deep neural network with a structural dynamic solver. Through learning the structure motion and fluid evolution in different fluid-structure interaction systems, the trained model can predict the fluid-structure interaction systems with different structural parameters only with initial flow field and structural motion conditions. Within the learned range of the parameters, the prediction accuracy of the fluid-structure interaction model is in good agreement with the numerical simulation results, which can meet the engineering needs. And the simulation speed is increased by more than twenty times, which is helpful for the rapid analysis and optimal design of fluid-structure interaction systems.

Yixing Wang

Papers

A novel spatial-temporal prediction method for unsteady wake flows based on hybrid deep neural network

Aerodynamic Coefficient Prediction of Airfoils with Convolutional Neural Network

Deep neural network based reduced-order model for fluid-structure interaction system

Aero-structural optimization of the HIRENASD Model configuration