Research

Applications

Inversion for optical properties of biological tissues in quantitative optoacoustic tomography
Bayesian optimal experimental design for inverse problems in acoustic scattering
Inversion and control for CO₂ sequestration with poroelastic models
Goal-oriented inference for reservoir models with complex features including faults
Joint seismic-electromagnetic inversion
Inference of basal boundary conditions for ice sheet flow
Inversion for coupled ice-ocean interaction
Inversion for material properties of cardiac tissue
Inference, prediction and optimization under uncertainty for turbulent combustion
Inference of constitutive laws in mechanics of nano-scale filaments

Publications

U. Villa, N. Petra, O. Ghattas, hIPPYlib: An extensible software framework for large-scale inverse problems; Part I: Deterministic inversion and linearized Bayesian inference, arXiv, 2019
P. Chen, U. Villa, O. Ghattas, Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty, Journal of Computational Physics, 385:163--186, 2019.
R. Nicholson, N. Petra and Jari P Kaipio. Estimation of the Robin coefficient field in a Poisson problem with uncertain conductivity field, Inverse Problems, Volume 34, Number 11, 2018.
P. Chen, K. Wu, J. Chen, T. O'Leary-Roseberry, O. Ghattas, Projected Stein Variational Newton: A Fast and Scalable Bayesian Inference Method in High Dimensions, arXiv, 2018
E. M. Constantinescu, N. Petra, J. Bessac, C. G. Petra, Statistical Treatment of Inverse Problems Constrained by Differential Equations-Based Models with Stochastic Terms, arXiv, 2018
U. Villa, N. Petra, O. Ghattas, hIPPYlib: An extensible software framework for large-scale inverse problems, Journal of Open Source Software (JOSS), 3(30):940, 2018
P. Chen, U. Villa, O. Ghattas, Taylor approximation for PDE-constrained optimization under uncertainty: Application to turbulent jet flow, Proceedings in Applied Mathematics and Mechanics - 89th GAMM Annual Meeting, 18:e201800466, 2018

Ph.D. Thesis

K. A. McCormack, Earthquakes, groundwater and surface deformation: exploring the poroelastic response to megathrust earthquakes, University of Texas at Austin, 2018. Adviser M. Hesse
B. Crestel, Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems, University of Texas at Austin, 2017. Adviser O. Ghattas

Oral Presentations

I. Ambartsumyan, O. Ghattas, Fast methods for Bayesian inverse problems governed by PDE forward models with random coefficient fields, Applied Inverse Problems Conference, July 8-12, 2019, Grenoble, France
U. Villa, O. Ghattas, Scalable optimal experimental design for large scale non-linear Bayesian inverse problems, Applied Inverse Problems Conference, July 8-12, 2019, Grenoble, France
O. Babaniyi, O. Ghattas, N. Petra and U. Villa, hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems, 2019 FEniCS Conference, Carnegie Institution for Science Department of Terrestrial Magnetism (DTM), Washington DC,June 12-14, 2019. Best postdoc presentation award
N. Petra, G. Stadler, Inverse Problems: Integrating Data with Models under Uncertainty, SIAM CSE, Feb 25-March 1, 2019, Spokane, Wa, US
K. Wu, P. Chen, O. Ghattas,A Stein Variational Newton Method for Optimal Experiment Design Problems, SIAM CSE, Feb 25-March 1, 2019, Spokane, Wa, US
P. Chen, O. Ghattas, U. Villa, Large-scale Optimal Experimental Design for Bayesian Nonlinear Inverse Problems, SIAM CSE, Feb 25-March 1, 2019, Spokane, Wa, US
T. O'Leary-Roseberry, J. Chen, P. Chen, U. Villa, O. Ghattas, Large-scale Optimization in Deep Learning for PDE Representation abstract, SIAM CSE, Feb 25-March 1, 2019, Spokane, Wa, US
J. J. Lee, O. Ghattas, T. Bui-Thanh, U. Villa, Derivative Informed MCMC Methods for Subsurface Models with Faults, SIAM CSE, Feb 25-March 1, 2019, Spokane, Wa, US
U. Villa, O. Ghattas, Scalable Methods for Bayesian Optimal Experimental Design Using Laplace Approximation, SIAM CSE, Feb 25-March 1, 2019, Spokane, Wa, US
U. Villa, Learning from data through the lens of mathematical models, Analysis Seminar, Dept. of Mathematics & Statistics, Washington University, January 28, 2019, St Louis, MO, US
U. Villa, Large Scale Inverse Problems and Uncertainty Quantification: Computational Tools and Imaging Applications, Electrical & Systems Engineering Seminar, Washington University, January 24, 2019, St Louis, MO, US
N. Petra, hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems, Optimization Seminar, University of California, Merced, October 19, 2018, Merced, CA, US
U. Villa, O. Ghattas, Maximize the Expected Information Gain in Bayesian Experimental Design Problems: A Fast Optimization Algorithm Based on Laplace Approximation and Randomized Eigensolvers, SIAM UQ, April 16-19, 2018, Garden Grove, CA, US
T. O’Leary-Roseberry, A PDE Constrained Optimization Approach to the Solution of the Stefan Problem, Texas Applied Mathematics and Engineering Symposium, Sept. 21-23, 2017, Austin, TX, US
U. Villa, hIPPYlib: An Extensible Software Framework for Large-Scale Deterministic and Linearized Bayesian Inverse, Texas Applied Mathematics and Engineering Symposium, Sept. 21-23, 2017, Austin, TX, US
U. Villa, Taylor Approximation for PDE-constrained Optimal Control Problems under High-dimensional Uncertainty, SIAM Control, July 10 - 12, 2017, Pittsburgh, Pa, US
U. Villa, Derivative-Informed MCMC for Bayesian Calibration of Stochastic PDE Models, SIAM Annual, July 10 - 14, 2017, Pittsburgh, Pa, US
U. Villa, Hessian-based sampling techniques for Bayesian inverse problems with stochastic PDE forward model, Applied Inverse Problems, May 29 - June 2, 2017, Hangzhou, China
U. Villa, Bayesian Calibration of Inadequate Stochastic PDE Models, SIAM CSE, Feb 27-March 3, 2017, Atlanta, GA, US
P. Chen, Taylor Approximation for PDE-Constrained Optimal Control Problems Under High-Dimensional Uncertainty: Application to a Turbulence Model, SIAM CSE, Feb 27-March 3, 2017, Atlanta, GA, US
B. Crestel, Scalable Solvers for Joint Inversion with Several Structural Coupling Terms, SIAM CSE, Feb 27-March 3, 2017, Atlanta, GA, US
Amal Alghamdi, Bayesian Inversion for Subsurface Properties from Poroelastic Forward Models and Surface Deformation Data, SIAM CSE, Feb 27-March 3, 2017, Atlanta, GA, US
U. Villa, An Analytical Technique for Forward and Inverse Propagation of Uncertainty, SIAM UQ, April 5-8, 2016, Lausanne, Switzerland

Poster Presentations

I. Ambartsumyan, T. Bui-Thanh, O. Ghattas, E. Khattatov, An Edge-preserving Method for Joint Bayesian Inversion with Non-Gaussian Priors, SIAM CSE, Feb 25- March 1, 2019, Spokane, Wa, US
E. Khattatov, O. Ghattas, T. Bui-Thanh, and I. Ambartsumyan, U. Villa, Bayesian Inversion of Fault Properties in Two-phase Flow in Fractured Media, SIAM CSE, Feb 25- March 1, 2019, Spokane, Wa, US
A. O. Babaniyi, O. Ghattas, N. Petra, U. Villa, hIPPYlib: An Extensible Software Framework for Large-scale Inverse Problems, SIAM CSE, Feb 25- March 1, 2019, Spokane, Wa, US
O. Ghattas, Y. Marzouk, M. Parno, N. Petra, U. Villa, Integrating Data with Complex Predictive Models under Uncertainty: An Extensible Software Framework for Large-Scale Bayesian Inversion, NSF-SI2 PI meeting, Apr. 30- May 1, 2018, Washington, DC, US
K. Koval, G. Stadler, Computational Approaches for Linear Goal-Oriented Bayesian Inverse Problems, SIAM Annual, July 10 - 14, 2017, Pittsburgh, Pa, US
J. Chen, A. Drach, U. Villa, R. Avazmohammadi, D. Li, O. Ghattas and M. Sacks, Identification of Mechanical Properties of 3D Myocardial Tissue: An Inverse Modeling and Optimal Experimental Design Problem, FEniCS'17, June 12-14, 2017, University of Luxembourg, Luxembourg
T. O’Leary-Roseberry, U. Villa, O. Ghattas, P. Heimbach, An Adjoint Capable Solver for the Stefan Problem: a Bilevel Optimization and Level Set Approach, SIAM CSE, Feb. 27 - March 3, 2017, Atlanta, GA, US
O. Ghattas, Y. Marzouk, M. Parno, N. Petra, U. Villa, Integrating Data with Complex Predictive Models under Uncertainty: An Extensible Software Framework for Large-Scale Bayesian Inversion, NSF-SI2 PI meeting, Feb. 21-22, 2017, Arlington, VA, US

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