Bishop's Lodge Ranch, Resort & Spa
Santa Fe, New Mexico
September 10-12, 2007

Many classes of problems in simulation-based science and engineering are characterized by a cycle of observation, parameter/state estimation, prediction, and decision-making. The critical steps in this process involve: (1) assimilating observational data into large-scale simulations to estimate uncertainties in input parameters, (2) propagation of those uncertainties through the simulation to predict output quantities of interest, and (3) determination of an optimal control or decision-making strategy taking into account the uncertain outputs. For many problems, the input parameters cannot be measured directly; instead they must be inferred from observations of simulation outputs. The estimation of input parameters and associated uncertainties from observations and from a computational model linking inputs to outputs constitutes a statistical inverse problem. The uncertainties in the input parameters result from observational errors, inadequate mathematical/computational models, and uncertain prior models of the inputs.

Characterization of the uncertainties in the inputs for high-dimensional parameter spaces and expensive forward simulations remains a tremendous challenge for many problems today. Yet despite their difficulties, there is a crucial unmet need for the development of scalable numerical algorithms for the solution of large-scale statistical inverse problems: uncertainty estimation in model inputs is a important precursor to the quantification of uncertainties underpinning prediction and decision-making. While complete quantification of uncertainty in inverse problems for very large scale nonlinear systems has been often intractable, several recent developments are making it viable: (1) the maturing state of algorithms and software for forward simulation for many classes of problems; (2) the imminent arrival of the petascale computing era; and (3) the explosion of available observational data in many scientific areas.

Accordingly, a workshop on Large-Scale Inverse Problems and Quantification of Uncertainty will be held September 10-12, 2007, in Santa Fe, New Mexico. The workshop is sponsored by the Computer Science Research Institute at Sandia National Labs, with additional funds provided by the National Science Foundation and the Air Force Office of Scientific Research. The workshop will focus on methods for estimation of uncertainty in the solution of inverse problems governed by large scale computer simulations, typically in the form of PDE models with uncertain inputs that are typically coefficients, initial conditions or system state, boundary conditions, sources, or other parameters of the PDEs.

The workshop will assess the current state-of-the-art and identify needs and opportunities for future research. 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 math, high performance computing, and forefront applications. The workshop will differ from previous events in its focus on algorithms and methods that offer scalability to very large scale problems, both in state and parameter space. The goal 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.

• Larry Biegler, Carnegie Mellon University
• George Biros, University of Pennsylvania
• Omar Ghattas, The University of Texas at Austin
• Matthias Heinkenschloss, Rice University
• David Keyes, Lawrence Livermore National Laboratory
• Bani Mallick, Texas A&M
• Luis Tenorio, Colorado School of Mines
• Bart van Bloemen Waanders, Sandia National Laboratories
• Karen Willcox, Massachusetts Institute of Technology