Reproducing kernel technique for high dimensional model representations (HDMR)

DOI10.1016/j.cpc.2014.07.021zbMath1360.46064OpenAlexW2033466521MaRDI QIDQ525724

Xiaopeng Luo, Xin Xu, Zhen-Zhou Lü

Publication date: 5 May 2017

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2014.07.021

zbMATH Keywords

modelingreproducing kernel Hilbert space (RKHS)high-dimensional function estimationhigh-dimensional model representations (HDMR)radial basis function (RBF) interpolation

Mathematics Subject Classification ID

Applications of functional analysis in quantum physics (46N50) Distributions, generalized functions, distribution spaces (46F99)

Related Items (5)

A numerical meshless method of soliton-like structures model via an optimal sampling density based kernel interpolation ⋮ On the fundamental conjecture of HDMR: a Fourier analysis approach ⋮ Improved Moving Least Square-Based Multiple Dimension Decomposition (MDD) Technique for Structural Reliability Analysis ⋮ Numerical meshless solution of high-dimensional sine-Gordon equations via Fourier HDMR-HC approximation ⋮ Adaptive sparse approximations of scattered data

Cites Work

• Tensor Decompositions and Applications
• General formulation of HDMR component functions with independent and correlated variables
• Metamodelling with independent and dependent inputs
• The smoothing effect of the ANOVA decomposition
• A recursive algorithm for finding HDMR terms for sensitivity analysis
• General foundations of high-dimensional model representations
• Efficient input-output model representations
• Error estimates and condition numbers for radial basis function interpolation
• A literature survey of low-rank tensor approximation techniques
• Radial Basis Functions
• Theory of Reproducing Kernels
• Efficient implementation of high dimensional model representations
• High dimensional model representations generated from low dimensional data samples. I: mp-cut-HDMR
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