A Graph Neural Network Surrogate Model for Multi-Objective Fluid-Acoustic Shape Optimization

Abstract: This article presents a graph neural network (GNN) based surrogate modeling approach for fluid-acoustic shape optimization. The GNN model transforms mesh-based simulations into a computational graph, enabling global prediction of pressure and velocity flow fields around solid boundaries. We employ signed distance functions to implicitly represent geometries on unstructured nodes represented by the graph neural network. The trained graph neural network is employed here to predict the flow field around various airfoil shapes. The median relative error in the prediction of pressure and velocity for 300 test cases is 1-2\%. The predicted flow field is employed to extract the fluid force coefficients and the velocity profile of the boundary layer. The boundary layer velocity profile is then used to predict the flow field and noise levels, allowing the direct integration of the coupled fluid-acoustic analysis in the shape optimization algorithm. The fluid-acoustic shape optimization is extended to multi-objective shape optimization by minimizing trailing edge noise while maximizing the aerodynamic performance of airfoil surfaces. The results show that the overall sound pressure level of the optimized airfoil decreases by 13.9\% (15.82 dBA), and the lift coefficient increases by 7.2\%, for a fixed set of operating conditions. The proposed GNN-based integrated surrogate modeling with the shape optimization algorithm exhibits a computational speed-up of three orders of magnitude compared to while maintaining reasonable accuracy compared to full-order online optimization applications. The GNN-based surrogate model offers an efficient computational framework for fluid-acoustic shape optimization via adaptive morphing of structures.