General foundations of high‐dimensional model representations

Keywords

Mathematics, Projection (relational algebra), Hierarchy, Euclidean space, Function (biology)

References

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• Statistical Mechanics: Principles and Selected ApplicationsTerrell L. Hill — 1987
• Constructive approximation : advanced problemsGeorge G. Lorentz, Manfred V. Golitschek, Yuly Makovoz — 1996
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• Functional Integrals: Approximate Evaluation and ApplicationsDenis Talay, A. D. Egorov, P. I. Sobolevsky — 1993
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• The Analysis of VarianceHenry Scheffé — 1960
• Importance measures in global sensitivity analysis of nonlinear modelsToshimitsu Homma, Andrea Saltelli — 1996
• Impact of heterogeneous reactions on stratospheric chemistry of the ArcticA. R. Douglass, R. S. Stolarski — 1989
• Optimal Global Rates of Convergence for Nonparametric RegressionCharles J. Stone — 1982
• Additive Regression and Other Nonparametric ModelsCharles J. Stone — 1985
• An efficient chemical kinetics solver using high dimensional model representationJeffrey A. Shorter, Precila C. Ip, Herschel Rabitz — 1999
• Inversion of experimental data to extract intermolecular and intramolecular potentialsTak-San Ho, Hershel Rabitz — 1993
• Projection Pursuit RegressionJerome H. Friedman, Werner Stuetzle — 1981
• Representation Properties of Networks: Kolmogorov's Theorem Is IrrelevantFederico Girosi, Tomaso Poggio — 1989

Cited by

• High dimensional model representation (HDMR) based folded vector decompositionLetİsya Dİvanyan, Metin Demi̇ralp — 2011
• Efficient chemical kinetic modeling through neural network maps.Thomas Eger, Petra Ebermann — 2004
• Surrogate modelling for the prediction of spatial fields based on simultaneous dimensionality reduction of high-dimensional input/output spacesEma Beatriz Carozzi Failde — 2018
• Diagnostic du colmatage des générateurs de vapeur à l'aide de modèles physiques et statistiquesSylvain Girard — 2012
• Novel Computational Methods for Solving High- Dimensional Random Eigenvalue ProblemsVaibhav Yadav — 2013
• An ab initio potential energy surface of the He H+2 → HeH++ H reactionWenwu Xu, Xinguo Liu, Shixia Luan — 2008
• Theoretical Studies on the ultrafast photodissociation of moleculesEmma Louise Chapman — 2009
• Numerical solution of ordinary differential equations via splinesNejla Altay, Metin Demi̇ralp — 2008
• Small scale high dimensional model representationEvrim Korkmaz, Metin Demi̇ralp — 2008
• Development of an interactive engineering design optimization frameworkAdam Cutbill — 2014
• Applications of flexibly initialized high dimensional model representation in computer visionEmre Demiralp — 2009
• Stationary fully probabilistic control designTatiana V. Guy, Miroslav Kárný — 2005
• Towards a new multiway array decomposition algorithm: elementwise multiway array high dimensional model representation (EMAHDMR)Muzaffer Ayvaz, Metin Demi̇ralp — 2011
• High dimensional model representation (HDMR) and trigonometric transformational HDMRNihal Şen, N. Abdülabki Baykara, Metin Demi̇ralp — 2008
• A generic reliability analysis and design framework with random parameter, field, and process variablesZhimin Xi — 2010
• High Dimensional Model Representations Generated from Low Dimensional Data Samples. I. mp-Cut-HDMRGenyuan Li, Shengwei Wang, C. M. Rosenthal — 2001
• Analytical Global Sensitivity Analysis and Uncertainty Propagation for Robust DesignWei Chen, Ruichen Jin, Agus Sudjianto — 2006
• Development, analysis, and evaluation of a commercial software framework for the study of Extremely Low Probability of Rupture (xLPR) events at nuclear power plants.Donald A. Kalinich, J.C. Helton, Cédric Sallaberry — 2010
• How additive are the Fourier series in the sense of high Dimensional model representationCaner Gülpinar, N. A. Baykara, Metin Demi̇ralp — 2008
• Metamodel-Based Global Optimization Methodologies for High Dimensional Expensive Black-box ProblemsKambiz Haji Hajikolaei — 2014

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