59 citations · 190 across the 27 of their papers we have counts for
41 papers
A Primer on the Karhunen-Loève Expansion
Alen Alexanderian
This article provides a primer on the spectral representation of random fields via the Karhunen-Loève Expansion (KLE). The goal is to bridge the gap between the theoretical foundat…
A new kernel-based approach for the global sensitivity analysis of models with correlated inputs
Troy Larsen, Alen Alexanderian
We present an HSIC-based approach for global sensitivity analysis of broad classes of models with correlated and possibly function-valued inputs and outputs. To this end, we define…
Robust optimal design of large-scale Bayesian nonlinear inverse problems
Abhijit Chowdhary, Ahmed Attia, Alen Alexanderian
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maxim…
Variance-based sensitivity of Bayesian inverse problems to the prior distribution
John E. Darges, Alen Alexanderian, Pierre A. Gremaud
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop…
Sensitivity Analysis of the Information Gain in Infinite-Dimensional Bayesian Linear Inverse Problems
Abhijit Chowdhary, Shanyin Tong, Georg Stadler +1
We study the sensitivity of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs) with respect to modeling uncertainties. In parti…
On Bayes risk of the posterior mean in linear inverse problems
Alen Alexanderian
We consider the concept of Bayes risk in the context of finite-dimensional ill-posed linear inverse problem with Gaussian prior and noise models. In this note, we rederive the foll…
A brief note on the Bayesian D-optimality criterion
Alen Alexanderian
We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of…
Optimal design of large-scale nonlinear Bayesian inverse problems under model uncertainty
Alen Alexanderian, Ruanui Nicholson, Noemi Petra
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we co…
A new perspective on parameter study of optimization problems
Alen Alexanderian, Joseph Hart, Mason Stevens
We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equa…
Hyper-differential sensitivity analysis for nonlinear Bayesian inverse problems
Isaac Sunseri, Alen Alexanderian, Joseph Hart +1
We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by PDEs with infinite-dimensional parameters. In previous works, HDSA has…
Extreme learning machines for variance-based global sensitivity analysis
John Darges, Alen Alexanderian, Pierre Gremaud
Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computation…
Global sensitivity analysis of rare event probabilities
Michael Merritt, Alen Alexanderian, Pierre Gremaud
By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the mod…
Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media
Helen Cleaves, Alen Alexanderian, Bilal Saad
We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimension…
Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don't know
Alen Alexanderian, Noemi Petra, Georg Stadler +1
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties,…
Monte Carlo Estimators for the Schatten p-norm of Symmetric Positive Semidefinite Matrices
Ethan Dudley, Arvind K. Saibaba, Alen Alexanderian
We present numerical methods for computing the Schatten -norm of positive semi-definite matrices. Our motivation stems from uncertainty quantification and optimal experimental d…
Optimal Experimental Design for Infinite-dimensional Bayesian Inverse Problems Governed by PDEs: A Review
Alen Alexanderian
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters.…
Global sensitivity analysis informed model reduction and selection applied to a Valsalva maneuver model
E. Benjamin Randall, Nicholas Z. Randolph, Alen Alexanderian +1
In this study, we develop a methodology for model reduction and selection informed by global sensitivity analysis (GSA) methods. We apply these techniques to a control model that t…
Multiscale global sensitivity analysis for stochastic chemical systems
Michael Merritt, Alen Alexanderian, Pierre A. Gremaud
Sensitivity analysis is routinely performed on simplified surrogate models as the cost of such analysis on the original model may be prohibitive. Little is known in general about t…
Hyper-Differential Sensitivity Analysis for Inverse Problems Constrained by Partial Differential Equations
Isaac Sunseri, Joseph Hart, Bart van Bloemen Waanders +1
High fidelity models used in many science and engineering applications couple multiple physical states and parameters. Inverse problems arise when a model parameter cannot be deter…
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs
Karina Koval, Alen Alexanderian, Georg Stadler
We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here,…
A distributed active subspace method for scalable surrogate modeling of function valued outputs
Hayley Guy, Alen Alexanderian, Meilin Yu
We present a distributed active subspace method for training surrogate models of complex physical processes with high-dimensional inputs and function valued outputs. Specifically,…
Randomization and reweighted -minimization for A-optimal design of linear inverse problems
Elizabeth Herman, Alen Alexanderian, Arvind K. Saibaba
We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average po…
Model input and output dimension reduction using Karhunen Loève expansions with application to biotransport
Alen Alexanderian, William Reese, Ralph C. Smith +1
We consider biotransport in tumors with uncertain heterogeneous material properties. Specifically, we focus on the elliptic partial differential equation (PDE) modeling the pressur…
Derivative-based global sensitivity analysis for models with high-dimensional inputs and functional outputs
Helen L. Cleaves, Alen Alexanderian, Hayley Guy +2
We present a framework for derivative-based global sensitivity analysis (GSA) for models with high-dimensional input parameters and functional outputs. We combine ideas from deriva…