45 citations · 147 across the 7 of their papers we have counts for
9 papers
Structure-Preserving Dimension Reduction and Surrogates for Partially Linear Bayesian Inverse Problems
Ziheng Zhang, Dingcheng Luo, Thomas O'Leary-Roseberry +2
Many Bayesian inverse problems are characterized by two parameter vectors with distinct roles. A medium property, operator coefficient, or geometry block enters the forward model n…
A note on the relationship between PDE-based precision operators and Matérn covariances
Umberto Villa, Thomas O'Leary-Roseberry
The purpose of this technical note is to summarize the relationship between the marginal variance and correlation length of a Gaussian random field with Matérn covariance and the c…
Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning
Thomas O'Leary-Roseberry, Peng Chen, Umberto Villa +1
We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to…
Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data Part II: Quantifying the Uncertainty
Amal Alghamdi, Marc Hesse, Jingyi Chen +2
Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduce…
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…
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…
Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty
Peng Chen, Umberto Villa, Omar Ghattas
In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty. Specifically, we consider a mean-…
Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
Peng Chen, Umberto Villa, Omar Ghattas
In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context o…
A data scalable augmented Lagrangian KKT preconditioner for large scale inverse problems
Nick Alger, Umberto Villa, Tan Bui-Thanh +1
Current state of the art preconditioners for the reduced Hessian and the Karush-Kuhn-Tucker (KKT) operator for large scale inverse problems are typically based on approximating the…