Research
Applications
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Inversion for optical properties of biological tissues in quantitative optoacoustic tomography
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Bayesian optimal experimental design for inverse problems in acoustic scattering
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Inversion and control for CO2 sequestration with poroelastic models
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Goal-oriented inference for reservoir models with complex features including faults
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Joint seismic-electromagnetic inversion
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Inference of basal boundary conditions for ice sheet flow
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Inversion for coupled ice-ocean interaction
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Inversion for material properties of cardiac tissue
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Inference, prediction and optimization under uncertainty for turbulent combustion
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Inference of constitutive laws in mechanics of nano-scale filaments
Publications
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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
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P. Chen, U. Villa, O. Ghattas, Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty, ArXiv, 2018
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U. Villa, N. Petra, O. Ghattas, hIPPYlib: An extensible software framework for large-scale inverse problems; Part I: Deterministic inversion and linearized Bayesian inference, in preparation, 2018
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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
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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, accepted, 2018
Ph.D. Thesis
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K. A. McCormack, Earthquakes, groundwater and surface deformation: exploring the poroelastic response to megathrust earthquakes, University of Texas at Austin, 2018. Adviser M. Hesse
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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
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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
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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
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N. Petra, hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems, Optimization Seminar, University of California, Merced, October 19, 2018, Merced, CA, US
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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
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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
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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
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U. Villa, Taylor Approximation for PDE-constrained Optimal Control Problems under High-dimensional Uncertainty, SIAM Control, July 10 - 12, 2017, Pittsburgh, Pa, US
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U. Villa, Derivative-Informed MCMC for Bayesian Calibration of Stochastic PDE Models, SIAM Annual, July 10 - 14, 2017, Pittsburgh, Pa, US
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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
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U. Villa, Bayesian Calibration of Inadequate Stochastic PDE Models, SIAM CSE, Feb 27-March 3, 2017, Atlanta, GA, US
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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
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B. Crestel, Scalable Solvers for Joint Inversion with Several Structural Coupling Terms, SIAM CSE, Feb 27-March 3, 2017, Atlanta, GA, US
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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
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U. Villa, An Analytical Technique for Forward and Inverse Propagation of Uncertainty, SIAM UQ, April 5-8, 2016, Lausanne, Switzerland
Poster Presentations
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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
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K. Koval, G. Stadler, Computational Approaches for Linear Goal-Oriented Bayesian Inverse Problems, SIAM Annual, July 10 - 14, 2017, Pittsburgh, Pa, US
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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
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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
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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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