In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity to additional meshing steps. The framework is validated on a benchmark ship.

翻译：在参数部分差异方程领域,由于需要的计算资源,形状优化是一个具有挑战性的问题。在这一贡献中,提议了一个数据驱动框架,涉及多种减少技术,以减少这种计算负担。正正正正正正正方形分解(POD)和主动子空间遗传算法(ASGA)用于原(高度忠诚)模型的尺寸减缩和基于主动次空间属性的有效遗传优化。形状的参数化直接应用于计算网格,利用辐射基函数(RBF)将适用于表面(优化对象)的一般变形图推广到网格节点。因此,原始网格的表面学和质量得到了保留,使基于POD的减序模型技术得以应用,并避免了额外网格步骤的必要性。框架在基准船上得到验证。