能否设计出完美的瑞士阿尔卑斯长号？基于缩减基方法和机器学习的形状优化组合
Can the perfect Swiss alphorn be designed? A combination of reduced basis method and machine learning for shape optimization
AI总结：
研究瑞士阿尔卑斯长号形状优化，通过实验测量和成像技术构建精确几何模型并网格化，引入几何参数化有限元公式结合缩减基方法生成模拟数据集，用于训练机器学习模型实现共振频率正逆向预测。
AI中文摘要：
在这项工作中，我们研究了瑞士阿尔卑斯长号的形状优化，以使其共振频率尽可能接近规定的目标音符。我们基于实验测量和成像技术构建了长号的精确几何模型，利用成像技术在无法直接测量的地方重建几何信息。所得三维模型采用全结构化方法进行网格划分。然后，我们引入了亥姆霍兹方程的几何参数化有限元公式，从而能够应用缩减基方法高效生成大量模拟数据集，其中每组几何参数对应一组特定的共振频率（音符）。该数据集可用于训练机器学习模型，以从几何参数正向预测共振频率，以及进行逆向设计，即估计几何形状以实现指定的目标音符。
英文摘要：
In this work, we investigate the shape optimization of a Swiss alphorn to achieve resonance frequencies as close as possible to prescribed target notes. We construct an accurate geometric model of the alphorn based on both experimental measurements and imaging techniques. The latter are used to reconstruct geometric information where direct measures are not available. The resulting 3D model is meshed using a fully structured approach. Then, we introduce a geometry-parametrized finite element (FE) formulation of the Helmholtz equation enabling the application of the Reduced Basis Method (RBM) to efficiently generate a large dataset of simulations, in which each set of geometric parameters corresponds to a specific set of resonance frequencies (notes). This dataset enables the training of machine learning (ML) models for forward prediction of resonance frequencies from geometric parameters, as well as inverse design, where geometries are estimated to achieve specified target notes.
