Research
Applications

Inversion for optical properties of biological tissues in quantitative optoacoustic tomography

Statistical treatment of inverse problems constrained by stochastic models

Accounting for model errors in inverse problems

Bayesian optimal experimental design for inverse problems in acoustic scattering

Inversion and control for CO_{2} sequestration with poroelastic models

Goaloriented inference for reservoir models with complex features including faults

Joint seismicelectromagnetic inversion

Inference of basal boundary conditions for ice sheet flow

Inversion for material properties of cardiac tissue

Inference, prediction and optimization under uncertainty for turbulent combustion
Selected publications

O. Babaniyi, R. Nicholson, U. Villa, and N. Petra: Inferring the basal sliding coefficient field for the Stokes ice sheet model under rheological uncertainty, The Cryosphere Discuss. [preprint], accepted, 2021.

U. Villa, N. Petra, O. Ghattas, hIPPYlib: An extensible software framework for largescale inverse problems; Part I: Deterministic inversion and linearized Bayesian inference, ACM Trans. Math. Softw. 47, 2, Article 16 (March 2021), 34 pages, 2021

A. Alghamdi, M.~A. Hesse, J. Chen, O. Ghattas, Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate, Water Resources Research, e2020WR027391, 2020

K. Koval, A. Alexanderian, G. Stadler, Optimal experimental design under irreducible uncertainty for inverse problems governed by PDEs, arXiv, 2019

S. Wahal, G. Biros, BIMC: The Bayesian Inverse Monte Carlo method for goaloriented uncertainty quantification. Part I, arXiv, 2019

S. Lan, Adaptive dimension reduction to accelerate infinitedimensional geometric Markov Chain Monte Carlo, Journal of Computational Physics, 392:7195, 2019

P. Chen, U. Villa, O. Ghattas, Taylor approximation and variance reduction for PDEconstrained optimal control under uncertainty, Journal of Computational Physics, 385:163186, 2019

B. Crestel, G. Stadler and O. Ghattas, A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs, Inverse Problems, 35:024003, 2018

A. Attia, A. Alexanderian, A. K. Saibaba, Goaloriented optimal design of experiments for largescale Bayesian linear inverse problems, Inverse Problems, 34:095009, 2018

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'LearyRoseberry, 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 EquationsBased Models with Stochastic Terms, arXiv, 2018

U. Villa, N. Petra, O. Ghattas, hIPPYlib: An extensible software framework for largescale inverse problems, Journal of Open Source Software (JOSS), 3(30):940, 2018

P. Chen, U. Villa, O. Ghattas, Taylor approximation for PDEconstrained optimization under uncertainty: Application to turbulent jet flow, Proceedings in Applied Mathematics and Mechanics  89th GAMM Annual Meeting, 18:e201800466, 2018

P. Chen, U. Villa, O. Ghattas, Hessianbased adaptive sparse quadrature for infinitedimensional Bayesian inverse problems, Computer Methods in Applied Mechanics and Engineering, 327:147172, 2017

S. Fatehiboroujeni, N. Petra and S. Goyal. Towards AdjointBased Inversion of the Lamé Parameter Field for Slender Structures With Cantilever Loading, ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 8: 28th Conference on Mechanical Vibration and Noise Charlotte, North Carolina, USA, August 21–24, 2016.
Selected Ph.D. thesis

A. Alghamdi, Bayesian Inverse Problems for QuasiStatic Poroelasticity with Application to Ground Water Aquifer Characterization from Geodetic Data, The University of Texas at Austin, 2020. Adviser O. Ghattas & M. Hesse

S. Fatehiboroujeni, Inverse Approaches for Identification of Constitutive Laws of Slender Structures Motivated by Application to Biological Filaments, University of California, Merced, 2018. Adviser S. Goyal

K. A. McCormack, Earthquakes, groundwater and surface deformation: exploring the poroelastic response to megathrust earthquakes, The University of Texas at Austin, 2018. Adviser M. Hesse

B. Crestel, Advanced techniques for multisource, multiparameter, and multiphysics inverse problems, The University of Texas at Austin, 2017. Adviser O. Ghattas
Selected Honor and Master thesis

B. Saleh, Scientific Machine Learning: A Neural NetworkBased Estimator for Forward Uncertainty Quantification, The University of Texas at Austin, 2018. Adviser O. Ghattas

G. Gao, hIPPYLearn: An inexact NewtonCG method for training neural networks with analysis of the Hessian, The University of Texas at Austin, 2017. Supervisor O. Ghattas

D. Liu, hIPPYLearn: An inexact stochastic NewtonCG method for training neural networks, The University of Texas at Austin, 2017. Supervisor O. Ghattas
Selected poster presentations

O. Ghattas, K. Kim, Y. Marzouk, M. Parno, N. Petra, U. Villa, Integrating Data with Complex Predictive Models under Uncertainty: An Extensible Software Framework for LargeScale Bayesian Inversion, NSFCSSI PI meeting, Feb. 1314, Seattle, Wa, US

I. Ambartsumyan, T. BuiThanh, O. Ghattas, E. Khattatov, An Edgepreserving Method for Joint Bayesian Inversion with NonGaussian Priors, SIAM CSE, Feb 25 March 1, 2019, Spokane, Wa, US

E. Khattatov, O. Ghattas, T. BuiThanh, and I. Ambartsumyan, U. Villa, Bayesian Inversion of Fault Properties in Twophase 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 Largescale 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 LargeScale Bayesian Inversion, NSFSI2 PI meeting, Apr. 30 May 1, 2018, Washington, DC, US

K. Koval, G. Stadler, Computational Approaches for Linear GoalOriented 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 1214, 2017, University of Luxembourg, Luxembourg

T. O’LearyRoseberry, 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 LargeScale Bayesian Inversion, NSFSI2 PI meeting, Feb. 2122, 2017, Arlington, VA, US
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