514 citations · 1.3k across the 26 of their papers we have counts for
34 papers
A Lipschitz Matrix for Parameter Reduction in Computational Science
Jeffrey M. Hokanson, Paul G. Constantine
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,…
A Lanczos-Stieltjes method for one-dimensional ridge function approximation and integration
Andrew Glaws, Paul G. Constantine
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 a…
Inverse regression for ridge recovery II: Numerics
Andrew Glaws, Paul G. Constantine, R. Dennis Cook
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 prov…
Gradient-based dimension reduction of multivariate vector-valued functions
Olivier Zahm, Paul Constantine, Clémentine Prieur +1
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We…
Exact active subspace Metropolis-Hastings, with applications to the Lorenz-96 system
Ingmar Schuster, Paul G. Constantine, T. J. Sullivan
We consider the application of active subspaces to inform a Metropolis-Hastings algorithm, thereby aggressively reducing the computational dimension of the sampling problem. We sho…
Gauss-Christoffel quadrature for inverse regression: applications to computer experiments
Andrew Glaws, Paul G. Constantine
Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functio…
Data-driven dimensional analysis: algorithms for unique and relevant dimensionless groups
Paul G. Constantine, Zachary del Rosario, Gianluca Iaccarino
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 dimensio…
Active subspaces of airfoil shape parameterizations
Zachary J. Grey, Paul G. Constantine
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-dimensi…
Data-driven polynomial ridge approximation using variable projection
Jeffrey M. Hokanson, Paul G. Constantine
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 a…
Randomized Learning of the Second-Moment Matrix of a Smooth Function
Armin Eftekhari, Michael B. Wakin, Ping Li +1
Consider an open set , equipped with a probability measure . An important characteristic of a smooth function $f:\mathbb{D}\rightarrow\mathbb{R}…
Dimension reduction in MHD power generation models: dimensional analysis and active subspaces
Andrew Glaws, Paul G. Constantine, John Shadid +1
Magnetohydrodynamics (MHD)---the study of electrically conducting fluids---can be harnessed to produce efficient, low-emissions power generation. Today, computational modeling assi…
Time-dependent global sensitivity analysis with active subspaces for a lithium ion battery model
Paul G. Constantine, Alireza Doostan
Renewable energy researchers use computer simulation to aid the design of lithium ion storage devices. The underlying models contain several physical input parameters that affect m…
A near-stationary subspace for ridge approximation
Paul G. Constantine, Armin Eftekhari, Jeffrey Hokanson +1
Response surfaces are common surrogates for expensive computer simulations in engineering analysis. However, the cost of fitting an accurate response surface increases exponentiall…
Many physical laws are ridge functions
Paul G. Constantine, Zachary del Rosario, Gianluca Iaccarino
A ridge function is a function of several variables that is constant along certain directions in its domain. Using classical dimensional analysis, we show that many physical laws a…
A Modified SEIR Model for the Spread of Ebola in Western Africa and Metrics for Resource Allocation
Paul Diaz, Paul Constantine, Kelsey Kalmbach +2
A modified, deterministic SEIR model is developed for the 2014 Ebola epidemic occurring in the West African nations of Guinea, Liberia, and Sierra Leone. The model describes the dy…
A randomized algorithm for enumerating zonotope vertices
Kerrek Stinson, David F. Gleich, Paul G. Constantine
We propose a randomized algorithm for enumerating the vertices of a zonotope, which is a low-dimensional linear projection of a hypercube. The algorithm produces a pair of the zono…
Density-Matching for Turbomachinery Optimization Under Uncertainty
Pranay Seshadri, Geoffrey Parks, Shahrokh Shahpar
A monotonic, non-kernel density variant of the density-matching technique for optimization under uncertainty is developed. The approach is suited for turbomachinery problems which,…
Global sensitivity metrics from active subspaces
Paul G. Constantine, Paul Diaz
Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to…
Accelerating MCMC with active subspaces
Paul G. Constantine, Carson Kent, Tan Bui-Thanh
The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its ite…
Computing Active Subspaces Efficiently with Gradient Sketching
Paul G. Constantine, Armin Eftekhari, Michael B. Wakin
Active subspaces are an emerging set of tools for identifying and exploiting the most important directions in the space of a computer simulation's input parameters; these direction…
A density-matching approach for optimization under uncertainty
Pranay Seshadri, Paul Constantine, Gianluca Iaccarino +1
Modern computers enable methods for design optimization that account for uncertainty in the system---so-called optimization under uncertainty. We propose a metric for OUU that meas…
Exploiting Active Subspaces to Quantify Uncertainty in the Numerical Simulation of the HyShot II Scramjet
Paul Constantine, Michael Emory, Johan Larsson +1
We present a computational analysis of the reactive flow in a hypersonic scramjet engine with focus on effects of uncertainties in the operating conditions. We employ a novel metho…
Computing active subspaces with Monte Carlo
Paul Constantine, David Gleich
Active subspaces can effectively reduce the dimension of high-dimensional parameter studies enabling otherwise infeasible experiments with expensive simulations. The key components…
Discovering an active subspace in a single-diode solar cell model
Paul G. Constantine, Brian Zaharatos, Mark Campanelli
Predictions from science and engineering models depend on the values of the model's input parameters. As the number of parameters increases, algorithmic parameter studies like opti…