论文标题
基于内核的活动子空间，并使用不连续的Galerkin方法应用于计算流体动力学参数问题
Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method
论文作者
论文摘要
主动子空间方法的非线性扩展为参数空间和响应表面设计的尺寸降低带来了显着的结果。我们进一步开发了一种基于内核的非线性方法。特别是，我们将其引入更广泛的数学框架中，该框架还考虑了多元目标函数参数空间的减少。与文献中已经存在的基准更具挑战性的基准，对实施进行了彻底的讨论和测试，文献中已经存在的基准，而活跃子空间的尺寸降低可以产生良好的结果。最后，在使用不连续的Galerkin方法求解的参数CFD应用程序的背景下，我们展示了使用新方法设计响应表面的整个管道。
Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions. The implementation is thoroughly discussed and tested on more challenging benchmarks than the ones already present in the literature, for which dimension reduction with active subspaces produces already good results. Finally, we show a whole pipeline for the design of response surfaces with the new methodology in the context of a parametric CFD application solved with the Discontinuous Galerkin method.
