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.

To alleviate the computational burden associated with the computational fluid dynamics (CFD) simulation stage and improve aerodynamic optimization efficiency, this work develops an innovative procedure for airfoil shape optimization, which is implemented through coupling the genetic algorithm (GA) optimizer with the aerodynamic coefficients prediction network (ACPN) model. The ACPN is established using a fully connected neural network with the airfoil geometry as the input and aerodynamic coefficients as the output. The results show that the ACPN's mean prediction accuracy for the lift and drag coefficient is high up to about 99.02%. Moreover, the prediction time of each aerodynamic coefficient is within 5 ms, four orders of magnitude faster compared to the CFD solver (3 min). Taking advantage of the fast and accurate prediction, the proposed ACPN model replaces the expensive CFD simulations and couples with GA to force the airfoil shape change to maximize the lift–drag ratio under multiple constraints. In terms of time efficiency, optimized airfoils can be fast obtained within 25 s. Even considering an extra 50 h spent on data preparing and 20 s for model training, the overall calculation cost is reduced by a remarkable 62.1% compared to the GA-CFD optimization method (5.5 days). Furthermore, the GA-ACPN model improves the lift–drag ratio with and without constraint by 51.4% and 55.4% for NACA0012 airfoil, respectively, while 50.3% and 60.0% improvement achieved by the GA-CFD optimization method. These results indicate that the GA-ACPN optimization approach significantly enhances the optimization efficiency and has great potential to address varying constraint optimization problems.