Knowledge-Constrained Shape Optimization with a Mixture-of-Experts Neural Operator for High-Confidence Design
This paper proposes a knowledge-constrained shape optimization framework that translates expert knowledge and user intent into quantifiable parameters for DFFD-based deformation operators. A Mixture-of-Experts Neural Operator (MoE-NO) improves drag prediction and trend consistency on heterogeneous datasets. Experiments show MoE-NO achieves 1.16% MAPE and 94.34% trend accuracy, with CFD-validated drag reductions of 4-10%.
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[Submitted on 7 Jul 2026]
Title:Knowledge-Constrained Shape Optimization with a Mixture-of-Experts Neural Operator for High-Confidence Design
View a PDF of the paper titled Knowledge-Constrained Shape Optimization with a Mixture-of-Experts Neural Operator for High-Confidence Design, by Wenhao Fan and 6 other authors
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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 $10\%$.
Subjects:
Computer Vision and Pattern Recognition (cs.CV); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
Cite as: arXiv:2607.09763 [cs.CV]
(or arXiv:2607.09763v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2607.09763
arXiv-issued DOI via DataCite
Submission history
From: Yuanwei Bin [view email] [v1] Tue, 7 Jul 2026 01:29:09 UTC (8,938 KB)
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