Velocity inversion: a case study in infinite-dimensional optimization
Mathematical Programming: Series A and B
Iterative solution methods
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Automatic Preconditioning by Limited Memory Quasi-Newton Updating
SIAM Journal on Optimization
A variational finite element method for source inversion for convective-diffusive transport
Finite Elements in Analysis and Design - Special issue: 14th Robert J. Melosh competition
High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Large-scale nonlinear optimization in circuit tuning
Future Generation Computer Systems
Goal-oriented, model-constrained optimization for reduction of large-scale systems
Journal of Computational Physics
Large-scale nonlinear optimization in circuit tuning
Future Generation Computer Systems
Numerical Algorithms for Polyenergetic Digital Breast Tomosynthesis Reconstruction
SIAM Journal on Imaging Sciences
A preconditioning technique for a class of PDE-constrained optimization problems
Advances in Computational Mathematics
Extreme-scale UQ for Bayesian inverse problems governed by PDEs
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Sundance: High-level software for PDE-constrained optimization
Scientific Programming
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One of the outstanding challenges of computational science and engineering is large-scale nonlinear parameter estimation of systems governed by partial differential equations. These are known as inverse problems, in contradistinction to the forward problems that usually characterize large-scale simulation. Inverse problems are significantly more difficult to solve than forward problems, due to ill-posedness, large dense ill-conditioned operators, multiple minima, space-time coupling, and the need to solve the forward problem repeatedly. We present a parallel algorithm for inverse problems governed by time-dependent PDEs, and scalability results for an inverse wave propagation problem of determining the material field of an acoustic medium. The difficulties mentioned above are addressed through a combination of total variation regularization, preconditioned matrix-free Gauss-Newton-Krylov iteration, algorithmic checkpointing, and multiscale continuation. We are able to solve a synthetic inverse wave propagation problem though a pelvic bone geometry involving 2.1 million inversion parameters in 3 hours on 256 processors of the Terascale Computing System at the Pittsburgh Supercomputing Center.