发表机构
Lancaster University（兰卡斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对贝叶斯形状优化需紧凑表达参数化的问题，提出从现有设计学习参数化的方法，经多类几何场景验证，该方法提升样本效率且可探索超出手动基线的范围。
AI 中文摘要
当目标函数昂贵且不可微时，贝叶斯优化是形状设计的自然工具，但它需要紧凑且具有表达力的搜索空间参数化。手动设计这样的参数化是一项复杂的工作，需要领域专业知识，且常产生隐式不可行区域、人工边界以及耦合无序坐标。我们转而从现有设计集合中学习参数化，对形状间的变形应用主成分分析，得到线性、可解释的搜索空间，其中主成分数量可在表达力与维度间明确权衡。在翼型、机翼和射频腔体上，涵盖从二维几何到三维空气动力学和电磁学的场景，我们展示了该方法提升的样本效率，以及探索超出手动设计基线范围的能力。
英文摘要
Bayesian optimisation is the natural tool for shape design when objectives are expensive and non-differentiable, but it needs a compact yet expressive parameterisation of the search space. Hand-crafting one is a complex endeavour requiring domain expertise, and often yields implicit infeasible regions, artificial bounds, and coupled, unordered coordinates. We instead learn the parameterisation from a collection of existing designs, applying principal component analysis to the deformations between shapes. The result is a linear, interpretable search space in which the number of components explicitly trades expressivity against dimensionality. Across aerofoils, wings, and radio-frequency cavities, spanning 2D geometry to 3D aerodynamics and electromagnetics, we show improved sample efficiency and the ability to explore beyond the confines of hand-crafted baselines.
