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 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 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 large-scale 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 goal-oriented uncertainty quantification. Part I, arXiv, 2019

• S. Lan, Adaptive dimension reduction to accelerate infinite-dimensional geometric Markov Chain Monte Carlo, Journal of Computational Physics, 392:71-95, 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

• 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, Goal-oriented optimal design of experiments for large-scale 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'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

• P. Chen, U. Villa, O. Ghattas, Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems, Computer Methods in Applied Mechanics and Engineering, 327:147-172, 2017

• S. Fatehiboroujeni, N. Petra and S. Goyal. Towards Adjoint-Based 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 Quasi-Static 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 multi-source, multi-parameter, and multi-physics inverse problems, The University of Texas at Austin, 2017. Adviser O. Ghattas

Selected Honor and Master thesis

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

• G. Gao, hIPPYLearn: An inexact Newton-CG 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 Newton-CG 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 Large-Scale Bayesian Inversion, NSF-CSSI PI meeting, Feb. 13-14, Seattle, Wa, US

• 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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