A graph neural network surrogate model for multi-objective fluid-acoustic shape optimization

This study presents a graph neural network (GNN)-based surrogate modeling approach for multi-objective fluid-acoustic shape optimization. The proposed GNN model transforms mesh-based simulations into a computational graph, enabling steady-state prediction of pressure and velocity fields around varying geometries subjected to different operating conditions. We employ signed distance functions to implicitly encode geometries on unstructured nodes represented by the graph neural network. By integrating these functions with computational mesh information into the GNN architecture, our approach effectively captures geometric variations and learns their influence on flow behavior. The trained graph neural network achieves high prediction accuracy for aerodynamic quantities, with median relative errors of 0.5%–1% for pressure and velocity fields across 200 test cases. The predicted flow field is utilized to extract fluid force coefficients and boundary layer velocity profiles, which are then integrated into an acoustic prediction model to estimate far-field noise. This enables the direct integration of the coupled fluid-acoustic analysis in the multi-objective shape optimization algorithm, where the airfoil geometry is optimized to simultaneously minimize trailing-edge noise and maximize aerodynamic performance. Results show that the optimized airfoil achieves a 13.9% reduction in overall sound pressure level (15.82 dBA) while increasing lift by 7.2% under fixed operating conditions. Optimization was also performed under a different set of operating conditions to assess the model’s robustness and demonstrate its effectiveness across varying flow conditions. In addition to its adaptability, our GNN-based surrogate model, integrated with the shape optimization algorithm, exhibits a computational speed-up of three orders of magnitude compared to full-order online optimization applications while maintaining high accuracy. This work demonstrates the potential of GNNs as an efficient data-driven approach for fluid-acoustic shape optimization via adaptive morphing of structures.