This paper applies deep reinforcement learning (DRL) on the synthetic jet control of flows over an NACA (National Advisory Committee for Aeronautics) 0012 airfoil under weak turbulent condition. Based on the proximal policy optimization method, the appropriate strategy for controlling the mass rate of a synthetic jet is successfully obtained at $Re=3000$ . The effectiveness of the DRL based active flow control (AFC) method is first demonstrated by studying the problem with constant inlet velocity, where a remarkable drag reduction of 27.0% and lift enhancement of 27.7% are achieved, accompanied by an elimination of vortex shedding. Then, the complexity of the problem is increased by changing the inlet velocity condition and reward function of the DRL algorithm. In particular, the inlet velocity conditions pulsating at two different frequencies and their combination are further applied, where the airfoil wake becomes more difficult to suppress dynamically and precisely; and the reward function additionally contains the goal of saving the energy consumed by the synergetic jets. After training, the DRL agent still has the ability to find a proper control strategy, where significant drag reduction and lift stabilization are achieved, and the agent with considerable energy saving is able to save the energy consumption of the synergetic jets for 83%. The performance of the DRL based AFC proves the strong ability of DRL to deal with fluid dynamics problems usually showing high nonlinearity and also serves to encourage further investigations on DRL based AFC.

In this paper, we propose a neural network based reduced-order model for predicting the unsteady flow field over single/multiple cylinders. The neural network model constructs a mapping function between the temporal evolution of the pressure signal on the cylinder surface and the surrounding velocity field, where Convolutional Neural Network (CNN) layers are used as the encoder and deconvolutional neural network layers are used as the decoder. Compared with the network model with a fully connected (FC) decoder, the model with the deconvolution connected (DC) decoder is good for capturing and reconstructing the spatial relationships of low-rank feature spaces, such as edge intersections, parallelism, and symmetry, while the fluid flow, which is described by Navier–Stokes equations containing convection and diffusion terms, displays outstanding features of locality. In this article, the performance of the network models with the FC decoder and the DC decoder is evaluated by studying the problem of flow over a single cylinder first, and then the complexity of the flow structure of the studied problems is enhanced by increasing the number of cylinders and the Reynolds number. The results indicate that both the CNN-FC decoder model and CNN-DC decoder model achieve fast and accurate prediction on the velocity field, and the CNN-DC decoder model gives more robust and precise performance for all studied problems.

In this article, we propose an unsteady data-driven reduced order model (ROM) (surrogate model) for predicting the velocity field around an airfoil. The network model applies a convolutional neural network (CNN) as the encoder and a deconvolutional neural network (DCNN) as the decoder. The model constructs a mapping function between temporal evolution of the pressure signal on the airfoil surface and the surrounding velocity field. For improving the model performance, the input matrix is designed to further incorporate the information of the Reynolds number, the geometry of the airfoil, and the angle of attack. The DCNN works as the decoder for better reconstructing the spatial and temporal information of the features extracted by the CNN encoder. The training and testing datasets of flow fields under different conditions are obtained by solving the Navier–Stokes equations using the computational fluid dynamics method. After model training, the neural network based ROM shows accurate and dramatically fast predictions on the flow field of the testing dataset with extended angles of attack and Reynolds numbers. According to the current study, the neural network-based ROM has exhibited attractive potentials on ROM of the unsteady fluid dynamic problem, and the model can potentially serve on investigating flow control or optimization problems in the future.

This paper introduces a novel surrogate model for two-dimensional adaptive steady-state thermal convection fields based on deep learning technology. The proposed model aims to overcome limitations in traditional frameworks caused by network types, such as the requirement for extensive training data, accuracy loss due to pixelated preprocessing of original data, and inability to predict information near the boundaries with precision. We propose a new framework that consists primarily of a physical-informed neural network (PINN) and a graph convolutional neural network (GCN). The GCN serves as the prediction module and predicts thermal convection in the two-dimensional computational domain by considering the mutual influence between unstructured nodes and their neighbors. On the other hand, the PINN acts as the physical constraint module of the framework by embedding the control equation of thermal convection into the loss function of the neural network, ensuring that the inference and prediction results of the GCN comply with the constraints of the control equation. The advantages of this framework lie in two aspects. First, the computation mechanism of the GCN is more in line with the actual evolution of temperature fields. Second, the PINN enhances the cognitive ability of the surrogate model toward the convection field information. It accurately describes the changes of temperature gradient information at the boundary position and reduces the model's demand for training data. To validate the advantages of the proposed model, we gradually analyzed the model's geometric adaptability and predictive accuracy from the single cylinder case to the double cylinder case. We also investigated the impact of the number of sampling points on model training and compared the model's prediction results with those of a purely data-driven model. The results show that the proposed model exhibits good geometric adaptability and stability. With only 20 training data, the mean error of the proposed model in predicting the velocity and temperature field is less than 1% and 0.6% for the single cylinder, and less than 2% and 1% for the double cylinder case, while the mean error of the purely data-driven GCN model in predicting the velocity and temperature field is 9.4% and 6.4% for the double cylinder case. These findings demonstrate the effectiveness of the proposed physics-informed graph convolutional neural network, allowing for more accurate prediction of fluid flow and heat convection using surrogate model.

In this paper, we proposed an innovative Bayesian optimization (BO) coupled with deep learning for rapid airfoil shape optimization to maximize aerodynamic performance of airfoils. The proposed aerodynamic coefficient prediction model (ACPM) consists of a convolutional path and a fully connected path, which enables the reconstruction of the end-to-end mapping between the Hicks–Henne (H–H) parameterized geometry and the aerodynamic coefficients of an airfoil. The computational fluid dynamics (CFD) model is first validated with the data in the literature, and the numerically simulated lift and drag coefficients were set as the ground truth to guide the model training and validate the network model based ACPM. The average accuracy of lift and drag coefficient predictions are both about 99%, and the determination coefficient R² are more than 0.9970 and 0.9539, respectively. Coupled with the proposed ACPM, instead of the conventional expensive CFD simulator, the Bayesian method improved the ratio of lift and drag coefficients by more than 43%, where the optimized shape parameters of the airfoil coincide well with the results by the CFD. Furthermore, the whole optimization time is less than 2 min, two orders faster than the traditional BO-CFD framework. The obtained results demonstrate the great potential of the BO-ACPM framework in fast and accurate airfoil shape optimization and design.

We propose a steady-state aerodynamic data-driven method to predict the incompressible flow around airfoils of NACA (National Advisory Committee for Aeronautics) 0012-series. Using the Signed Distance Function (SDF) to parameterize the geometric and flow condition setups, the prediction core of the method is constructed essentially by a consecutive framework of a convolutional neural network (CNN) and a deconvolutional neural network (DCNN). Impact of training parameters on the behavior of the proposed CNN-DCNN model is studied, so that appropriate learning rate, mini-batch size, and random deactivation rate are specified. Tested by “unseen” airfoil geometries and far-field velocities, it is found that the prediction process is three orders of magnitudes faster than a corresponding Computational Fluid Dynamics (CFD) simulation, while relative errors are maintained lower than 1% on most of the sample points. The proposed model manages to capture the essential dynamics of the flow field, as its predictions correspond reasonably with the reconstructed field by proper orthogonal decomposition (POD). The performance and accuracy of the proposed model indicate that the deep learning-based approach has great potential as a robust predictive tool for aerodynamic design and optimization.