A comprehensive deep learning geometric shape optimization framework with field prediction surrogate and reinforcement learning

The optimization of aerodynamic components' geometric shapes demands a novel technical approach for adaptive and efficient exploration and decision-making within the design space. In this study, we introduce an innovative shape optimization framework that leverages deep reinforcement learning with neural network surrogate models. The field prediction surrogate, realized by two distinct U-net architectures, can efficiently generate holistic field solutions based on the transformed mesh coordinates. Subsequently, an inference engine dynamically calculates the key metric of the flow fields, serving as the objective function for the subsequent geometry-aware Deep Q network (DQN)-based optimization. The framework's efficacy is validated using a rocket nozzle as an illustrative example. During surrogate validation, under both friction and frictionless conditions, the l 1 errors of the entire flow field of both the U-net vision transformer (ViT) and U-net convolutional neural network (CNN) architectures are less than 0.4%. The proposed U-net ViT consistently outperforms U-net CNN, and the superiority is particularly evident in complex flow areas, outlet sections, and vacuum thrust prediction. Following training, the DQN model is employed to explore the design variable space. The B-spline defining profile successfully is optimized to a final expanding segment shape with improved thrust. Under frictionless conditions, it closely approaches the theoretical optimum. In the practical condition considering friction, the optimized shape gains a 2.96% thrust improvement. The results demonstrate that the proposed framework, especially when coupled with U-net ViT, exhibits enhanced accuracy and adaptability for shape optimization tasks.