Gradient-Based Dimension Reduction of Multivariate Vector-Valued Functions

DOI10.1137/18M1221837zbMath1433.41007arXiv1801.07922MaRDI QIDQ5220403

Olivier Zahm, Youssef M. Marzouk, Paul G. Constantine, Clémentine Prieur

Publication date: 20 March 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.07922

zbMATH Keywords

dimension reductionPoincaré inequalityhigh-dimensional function approximationSobol' indicesactive subspaceridge approximation

Mathematics Subject Classification ID

Multidimensional problems (41A63) Algorithms for approximation of functions (65D15) Approximation by other special function classes (41A30)

Related Items (23)

Preintegration via Active Subspace ⋮ Reduced basis methods for time-dependent problems ⋮ Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems ⋮ Certified dimension reduction in nonlinear Bayesian inverse problems ⋮ Characterization of flow through random media via Karhunen-Loève expansion: an information theory perspective ⋮ Generalized bounds for active subspaces ⋮ Model Reduction for Nonlinear Systems by Balanced Truncation of State and Gradient Covariance ⋮ Learning high-dimensional parametric maps via reduced basis adaptive residual networks ⋮ Kernel‐based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method ⋮ Multifidelity Dimension Reduction via Active Subspaces ⋮ On the Deep Active-Subspace Method ⋮ Multi‐fidelity data fusion through parameter space reduction with applications to automotive engineering ⋮ Large-scale Bayesian optimal experimental design with derivative-informed projected neural network ⋮ Derivative-informed neural operator: an efficient framework for high-dimensional parametric derivative learning ⋮ An efficient dimension reduction for the Gaussian process emulation of two nested codes with functional outputs ⋮ Modified Active Subspaces Using the Average of Gradients ⋮ A distributed active subspace method for scalable surrogate modeling of function valued outputs ⋮ Embedded ridge approximations ⋮ Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs ⋮ Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media ⋮ Derivative-Based Global Sensitivity Analysis for Models with High-Dimensional Inputs and Functional Outputs ⋮ A Supervised Learning Approach Involving Active Subspaces for an Efficient Genetic Algorithm in High-Dimensional Optimization Problems ⋮ Data-free likelihood-informed dimension reduction of Bayesian inverse problems

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