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

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 CFD application solved with the Discontinuous Galerkin method.

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• A multi-fidelity approach coupling parameter space reduction and non-intrusive POD with application to structural optimization of passenger ship hulls
• A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems
• Enhancing CFD predictions in shape design problems by model and parameter space reduction
• ATHENA: Advanced Techniques for High Dimensional Parameter Spaces to Enhance Numerical Analysis
• A Dimensionality Reduction Approach for Convolutional Neural Networks
• Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method
• Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering
• A local approach to parameter space reduction for regression and classification tasks
• Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces
• Surrogate to Poincaré inequalities on manifolds for dimension reduction in nonlinear feature spaces