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IMA Annual Program Year Workshop

Large-scale Inverse Problems and Quantification of Uncertainty

Large-scale Inverse Problems and Quantification of Uncertainty

June 6-10, 2011

University of Texas, Austin | |

University of Texas, Austin | |

Colorado School of Mines | |

Massachusetts Institute of Technology |

Many classes of problems in computational science and engineering are characterized
by a cycle of experiment design, observation, parameter/state estimation, prediction, and
decision-making. The critical steps in this process involve: (1) modeling of the physical
processes via, for example, PDEs; (2) estimating unknown parameters in the model from
observational data via solution of an inverse problem; (3) propagation of input uncertainties
through the model to issue predictions; and (4) determination of an optimal control or
decision-making strategy that takes into account the uncertain outputs. The estimation of
unknown model parameters or state from observational data, together with a model linking
inputs to outputs, constitutes an inverse problem; it is called a statistical inverse problem
when at least one of the components in this process is modeled as random. Data assimilation
and joint inversion are two particular settings that have a wide range of applications.
In many cases of current scientific and industrial interest, solution of the statistical in-
verse problem remains prohibitive, particularly for high-dimensional parameter spaces and
expensive forward models. The use of established numerical and statistical methods that
have become routine for small or moderate-sized problems poses challenges for large-scale
problems. Yet despite this difficulty, there is a crucial need for the development of scalable
algorithms for the solution of large-scale statistical inverse problems: uncertainty estimation
in model parameters and state is an important precursor to the quantification of uncertainties
underpinning prediction and decision-making. While complete quantification of uncertainty
in inverse problems for large-scale nonlinear systems has been often intractable, several re-
cent developments are making it viable: (1) the maturing state of algorithms and software for
forward simulation for many classes of problems; (2) the arrival of the petascale computing
era; (3) new advances in Bayesian computing; and (4) the explosion of available observational
data in many scientific areas.
This workshop will assess the current state-of-the-art and identify needs and opportunities for future research at the intersection of large-scale inverse problems and uncertainty quantification. It will bring together and cross-fertilize the perspectives of researchers in the areas of inverse problems and data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and forefront applications. The goal of the workshop will be to identify promising future directions for resolving the difficulties associated with high-dimensional statistical inverse problems, and opportunities in such areas as the aerospace, astrophysical, biomedical, chemical, energy, geological, industrial, mechanical, and petroleum engineering and sciences. Participants will be solicited broadly from academia, government laboratories, and industry.