Research

Applications

Inference, prediction and optimization under uncertainty for turbulent combustion
Inversion and control for CO₂ sequestration with poroelastic models
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 of constitutive laws in mechanics of nano-scale filaments

Publications

P. Chen, U. Villa, O. Ghattas, Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty, ArXiv, 2018
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

Ph.D. Thesis

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

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

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