171 citations · 211 across the 10 of their papers we have counts for
17 papers
Adjoint-based Inversion for the Diffusion Coefficient in Marine Lake Models
Alex Ho, François Blanchette, Noémi Petra +1
Marine lakes offer a unique opportunity to study how physical processes, such as turbulent mixing, biomixing, and tidal exchanges, regulate the vertical transport of heat, oxygen,…
A Scalable Interior-Point Gauss-Newton Method for PDE-Constrained Optimization with Bound Constraints
Tucker Hartland, Cosmin G. Petra, Noemi Petra +1
We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a r…
Point spread function approximation of high rank Hessians with locally supported non-negative integral kernels
Nick Alger, Tucker Hartland, Noemi Petra +1
We present an efficient matrix-free point spread function (PSF) method for approximating operators that have locally supported non-negative integral kernels. The method computes im…
Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initializaiton
Tucker Hartland, Georg Stadler, Mauro Perego +2
Obtaining lightweight and accurate approximations of Hessian applies in inverse problems governed by partial differential equations (PDEs) is an essential task to make both determi…
Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models
Terrence Alsup, Tucker Hartland, Benjamin Peherstorfer +1
Multilevel Stein variational gradient descent is a method for particle-based variational inference that leverages hierarchies of surrogate target distributions with varying costs a…
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…
hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty
Ki-Tae Kim, Umberto Villa, Matthew Parno +3
Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the…
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,…
hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized Bayesian Inference
Umberto Villa, Noemi Petra, Omar Ghattas
We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) wit…
Statistical Treatment of Inverse Problems Constrained by Differential Equations-Based Models with Stochastic Terms
Emil M. Constantinescu, Noemi Petra, Julie Bessac +1
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution repres…
Estimation of the Robin coefficient field in a Poisson problem with uncertain conductivity field
Ruanui Nicholson, Noemi Petra, Jari Kaipio
We consider the reconstruction of a heterogeneous coefficient field in a Robin boundary condition on an inaccessible part of the boundary in a Poisson problem with an uncertain (or…
A Bayesian Approach for Parameter Estimation with Uncertainty for Dynamic Power Systems
Noemi Petra, Cosmin G. Petra, Zheng Zhang +2
We address the problem of estimating the uncertainty in the solution of power grid inverse problems within the framework of Bayesian inference. We investigate two approaches, an ad…
Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximations
Alen Alexanderian, Noemi Petra, Georg Stadler +1
We present a method for optimal control of systems governed by partial differential equations (PDEs) with uncertain parameter fields. We consider an objective function that involve…
A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems
Alen Alexanderian, Noemi Petra, Georg Stadler +1
We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by PDEs. The goal is to find a placement of sensors, at which experimen…
Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet
Tobin Isaac, Noemi Petra, Georg Stadler +1
The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem: given parameter inputs, solve the governi…
A computational framework for infinite-dimensional Bayesian inverse problems: Part II. Stochastic Newton MCMC with application to ice sheet flow inverse problems
Noemi Petra, James Martin, Georg Stadler +1
We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we c…
A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized -sparsification
Alen Alexanderian, Noemi Petra, Georg Stadler +1
We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PD…