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 computational fluid dynamics application solved with the discontinuous Galerkin method.

Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method / Romor, F; Tezzele, M; Lario, A; Rozza, G. - In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING. - ISSN 0029-5981. - 123:23(2022), pp. 6000-6027. [10.1002/nme.7099]

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

Romor, F;Tezzele, M;Lario, A;Rozza, G
2022

Abstract

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 computational fluid dynamics application solved with the discontinuous Galerkin method.
123
23
6000
6027
10.1002/nme.7099
https://arxiv.org/abs/2008.12083
Romor, F; Tezzele, M; Lario, A; Rozza, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/130150
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