Engineering shape optimization faces challenges related to expert-dependent problem setups and surrogate model reliability. In practical aerodynamic design, optimization settings such as editable regions, deformation ranges, and design-preservation constraints are typically specified manually by experienced engineers. However, surrogate-based optimization may become unreliable for heterogeneous geometry databases and out-of-distribution designs. To address these challenges, we propose a knowledge-constrained shape optimization framework that translates knowledge-based constraints and user intent into quantifiable parameters of DFFD-based deformation operators, enabling engineering-aware and controllable constrained optimization.
We further develop a Mixture-of-Experts Neural Operator (MoE-NO) to improve drag prediction and trend consistency over heterogeneous aerodynamic datasets. Based on the MoE-NO encoder and Mahalanobis distance, an uncertainty estimation strategy is introduced to detect out-of-distribution geometries and selectively trigger physics-solver feedback for local sample enrichment.
Experiments on in-house MPV, SUV, and Sedan datasets show that MoE-NO achieves a test-set MAPE of $1.16\%$ and a trend-prediction accuracy of $94.34\%$, outperforming the best baseline results of $1.52\%$ and $90.34\%$, respectively. Vehicle shape-optimization experiments further yield CFD-validated drag coefficient reductions of approximately $4\%$ to $10\%$.
Blogger's Review: This study significantly enhances drag prediction accuracy and trend consistency in aerodynamic design via the introduction of a Mixture-of-Experts Neural Operator, highlighting the importance of knowledge constraints in shape optimization. Future research could explore applying this method in more complex design spaces.