Knowledge-Constrained Shape Optimization with a Mixture-of-Experts Neural Operator for High-Confidence Design

2026-07-06

AI Summary

This work addresses the limitations of conventional engineering shape optimization, which often relies on expert-defined constraints and suffers from unreliable surrogate models when handling heterogeneous geometries or out-of-distribution designs. To overcome these challenges, the authors propose a knowledge-constrained shape optimization framework that explicitly embeds engineering knowledge and user intent into the DFFD-based deformation parameterization, thereby constructing interpretable geometric constraints. The framework further integrates a Mixture-of-Experts neural operator to enhance aerodynamic performance prediction accuracy and employs a Mahalanobis distance–based uncertainty estimation mechanism to trigger high-fidelity CFD feedback for designs lying outside high-confidence regions. Evaluated on MPV, SUV, and Sedan datasets, the method achieves a mean absolute percentage error of 1.16% and a trend prediction accuracy of 94.34%, yielding drag coefficient reductions of 4%–10% and significantly improving both optimization efficiency and reliability.

Abstract

Engineering shape optimization faces challenges in both expert-dependent problem setup 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, while 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 $10\%$.

Problem

• shape optimization
• surrogate-model reliability
• expert-dependent setup
• out-of-distribution designs
• aerodynamic design

Innovation

• Mixture-of-Experts Neural Operator
• knowledge-constrained optimization
• DFFD-based deformation
• uncertainty estimation
• aerodynamic shape optimization