arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2008.12083math.NAcs.NA
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基于核的主动子空间及其在使用间断Galerkin方法的计算流体动力学参数问题中的应用

Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method

Francesco Romor, Marco Tezzele, Andrea Lario, Gianluigi Rozza

AI总结:

本文发展了一种基于核的非线性主动子空间方法,将其引入多元目标函数参数空间降维的数学框架,并通过间断Galerkin方法的CFD应用展示了响应面设计的完整流程。

摘要:

主动子空间方法的非线性扩展在参数空间降维和响应面设计中带来了显著成果。我们进一步发展了一种基于核的非线性方法。特别地,我们将其引入一个更广泛的数学框架中,该框架还考虑了多元目标函数在参数空间中的降维。我们对其实现进行了充分讨论,并在比现有文献中更具挑战性的基准上进行了测试,对于这些基准,使用主动子空间进行降维已经产生了良好的结果。最后,我们展示了在用间断Galerkin方法求解的参数化CFD应用背景下,使用新方法设计响应面的完整流程。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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