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.
Keywords: active subspaces; dimension reduction; discontinuous Galerkin; kernel methods; ridge approximation.
© 2022 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.