The three-day workshop will be held on September 10-12, 2007, at the Bishop?s Lodge near Santa Fe, NM, site of our two previous workshops. The number of participants will be limited to 50, all invited, to create an optimal environment for discussion and discourse. In addition, another 10 participants will be drawn from an applicant pool of postdocs and students.
Intellectual Merits. Many classes of problems in simulation-based science and engineering are characterized by a cycle of observation, data assimilation, 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 computational models, and uncertain prior models of the inputs, and Bayesian inference often plays a central role. 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 an important precursor of the quantification of uncertainties underpinning prediction and decision-making. While in the past, full and rigorous quantification of uncertainty in inverse problems and data assimilation for large scale systems has been intractable, several recent developments are making this enterprise viable: (1) the maturing state of algorithms and software for forward simulation, and their availability in the form of community codes, for many classes of problems in science and engineering; (2) the arrival of the petascale computing age; and (3) the explosion of observational data, much of it archived and accessible over data grids.
Broader impacts.
Accordingly, the P.I. proposes to organize a workshop dedicated to uncertainty estimation for large-scale models that will capitalize on these three Cyberinfrastructure developments. The workshop will assess the current state-of-the-art and identify needs and opportunities for future research. Leading figures in larges scale statistical inversion and data assimilation will be invited, along with promising junior investigators, postdocs, and students. The workshop will bring together and cross-fertilize the perspectives of researchers in the areas of large scale optimization, statistics, inverse problems, applied and computational math, high performance computing, and forefront applications. The focus will be on methods to characterize uncertainty in inputs (typically coefficients, initial conditions or system state, boundary conditions, sources, or other parameters of PDE models) via solution of statistical inverse problems. The workshop will differ from previous workshops in its focus on algorithms and methods that offer scalability to very large-scale models and simulations. The workshop will encourage the exchange of ideas, discuss outstanding unresolved barriers, present general solution strategies, establish future collaborations, and initiate new algorithmic directions. The goal will be to identify the path forward for resolving the difficulties associated with high-dimensional statistical inverse problems, and opportunities in such areas as aerospace, astrophysics, biomedical, chemical, geological, industrial, mechanical, and petroleum engineering and sciences.
