171 citations · 898 across the 46 of their papers we have counts for
13 papers · 1 filter
Nonuniform 3D finite difference elastic wave simulation on staggered grids
Longfei Gao, Omar Ghattas, David Keyes
We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulat…
Taylor approximation for chance constrained optimization problems governed by partial differential equations with high-dimensional random parameters
Peng Chen, Omar Ghattas
We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-di…
Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities
Peng Chen, Keyi Wu, Omar Ghattas
We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVI…
Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEs
Thomas O'Leary-Roseberry, Umberto Villa, Peng Chen +1
Many-query problems, arising from uncertainty quantification, Bayesian inversion, Bayesian optimal experimental design, and optimization under uncertainty-require numerous evaluati…
A globally convergent modified Newton method for the direct minimization of the Ohta-Kawasaki energy with application to the directed self-assembly of diblock copolymers
Lianghao Cao, Omar Ghattas, J. Tinsley Oden
We propose a fast and robust scheme for the direct minimization of the Ohta-Kawasaki energy that characterizes the microphase separation of diblock copolymer melts. The scheme empl…
A fast and scalable computational framework for large-scale and high-dimensional Bayesian optimal experimental design
Keyi Wu, Peng Chen, Omar Ghattas
We develop a fast and scalable computational framework to solve large-scale and high-dimensional Bayesian optimal experimental design problems. In particular, we consider the probl…
Optimal design of acoustic metamaterial cloaks under uncertainty
Peng Chen, Michael R. Haberman, Omar Ghattas
In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. Th…
Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs
Ilona Ambartsumyan, Wajih Boukaram, Tan Bui-Thanh +5
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for…
Stein variational reduced basis Bayesian inversion
Peng Chen, Omar Ghattas
We propose and analyze a Stein variational reduced basis method (SVRB) to solve large-scale PDE-constrained Bayesian inverse problems. To address the computational challenge of dra…
Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate
Amal Alghamdi, Marc A. Hesse, Jingyi Chen +1
Characterizing the properties of groundwater aquifers is essential for predicting aquifer response and managing groundwater resources. In this work, we develop a high-dimensional s…
Ill-Posedness and Optimization Geometry for Nonlinear Neural Network Training
Thomas O'Leary-Roseberry, Omar Ghattas
In this work we analyze the role nonlinear activation functions play at stationary points of dense neural network training problems. We consider a generic least squares loss functi…
Projected Stein Variational Gradient Descent
Peng Chen, Omar Ghattas
The curse of dimensionality is a longstanding challenge in Bayesian inference in high dimensions. In this work, we propose a projected Stein variational gradient descent (pSVGD) me…
Low Rank Saddle Free Newton: A Scalable Method for Stochastic Nonconvex Optimization
Thomas O'Leary-Roseberry, Nick Alger, Omar Ghattas
In modern deep learning, highly subsampled stochastic approximation (SA) methods are preferred to sample average approximation (SAA) methods because of large data sets as well as g…