Zobrazeno 1 - 10
of 159
pro vyhledávání: '"CONSTANTINE, PAUL"'
Publikováno v:
SIAM Journal on Scientific Computing Vol. 43, No. 3, pp. A1858--A1880 (2021)
We introduce the Lipschitz matrix: a generalization of the scalar Lipschitz constant for functions with many inputs. Among the Lipschitz matrices compatible a particular function, we choose the smallest such matrix in the Frobenius norm to encode the
Externí odkaz:
http://arxiv.org/abs/1906.00105
Autor:
Glaws, Andrew, Constantine, Paul G.
Many of the input-parameter-to-output-quantity-of-interest maps that arise in computational science admit a surprising low-dimensional structure, where the outputs vary primarily along a handful of directions in the high-dimensional input space. This
Externí odkaz:
http://arxiv.org/abs/1808.02095
We investigate the application of sufficient dimension reduction (SDR) to a noiseless data set derived from a deterministic function of several variables. In this context, SDR provides a framework for ridge recovery. In this second part, we explore t
Externí odkaz:
http://arxiv.org/abs/1802.01541
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these directions and us
Externí odkaz:
http://arxiv.org/abs/1801.07922
We consider the application of active subspaces to inform a Metropolis-Hastings algorithm, thereby aggressively reducing the computational dimension of the sampling problem. We show that the original formulation, as proposed by Constantine, Kent, and
Externí odkaz:
http://arxiv.org/abs/1712.02749
Autor:
Glaws, Andrew, Constantine, Paul G.
Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functions of several variables such as those arising in computer experiments.
Externí odkaz:
http://arxiv.org/abs/1710.01372
Classical dimensional analysis has two limitations: (i) the computed dimensionless groups are not unique, and (ii) the analysis does not measure relative importance of the dimensionless groups. We propose two algorithms for estimating unique and rele
Externí odkaz:
http://arxiv.org/abs/1708.04303
Publikováno v:
SIAM J. Sci. Comput. 40(3) A1566-A1589, 2018
Inexpensive surrogates are useful for reducing the cost of science and engineering studies involving large-scale, complex computational models with many input parameters. A ridge approximation is one class of surrogate that models a quantity of inter
Externí odkaz:
http://arxiv.org/abs/1702.05859
Autor:
Grey, Zachary J., Constantine, Paul G.
Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in
Externí odkaz:
http://arxiv.org/abs/1702.02909
Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction (SDR) use data
Externí odkaz:
http://arxiv.org/abs/1702.02227