Uncertainty Quantification for Systems Governed by Partial Differential Equations; May 2010; Edinburgh, Scotland

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In deterministic modeling, complete knowledge of input parameters is assumed. This leads to simplified, tractable computations and produces simulations of outputs that correspond to specific choices of inputs. However, most physical, biological, social, economic, financial, etc. processes involve some degree of uncertainty. Uncertainty quantification (UQ) is the task of determining statistical information about the outputs of a process of interest, given only statistical (i.e., incomplete) information about the inputs. The particular focus of the workshop are processes governed by partial differential equations (PDEs). It has long been recognized that mathematical models need to account for such uncertainties. However, the science of UQ in many application areas is still in its infancy. There is much current activity in disparate areas of mathematics, statistics, science, and engineering that is relevant to UQ. However, fundamental and challenging mathematical issues remain unsolved, in particular combating the "curse of dimensionality" attendant to solving problems in high dimensions remains an unresolved issue. The workshop is meant to help ameliorate this situation. The workshop brings together experts in all areas of mathematics and statistics relevant to UQ as well as scientists and engineers working in application areas. The objectives of the workshop are as follows: to review developments in this rapidly developing field; to bring together internationally leading experts working in relevant fields of mathematics, statistics, and other areas and enable an effective dialogue between them; to expose industrial researchers to the recent developments in the field and mathematical scientists to the important problems facing industry; to promote communication between the various relevant mathematical disciplines (e.g., numerical analysis, probability theory, statistics, high-performance computing); to encourage junior researchers to work in the field; and to strengthen interactions between researchers coming from different areas of research. The workshop commences with three short courses that are meant to get everyone up to speed on the disparate aspects of UQ and stochastic PDEs considered in the workshop. Although the short courses are of value for everyone attending the workshop, they are especially valuable for junior researchers. The workshop closes with a session devoted to a discussion of future directions in stochastic PDE and UQ research with a special emphasis on the outstanding open problems that need to be solved in order to make stochastic PDE-based UQ a tool that is easily, routinely, and readily available to those in government and industry that have to make decisions in environments involving risk and uncertainty. Uncertainty quantification (UQ) is the process of accurately assessing the uncertainties in predictions made by scientists and engineers about physical, biological, social, economic, financial, military, etc. processes. For example, predicting hurricane paths, the structural integrity of a bridge or airplane, future prices of financial instruments, and the lifetime to failure of military equipment are all subject to uncertainty. Thus, accurately quantifying that uncertainty is of paramount importance to engineers in the design process, to government officials when making policy decisions including those related to homeland security and military strategies, to response teams assessing dangers and remedies in natural and man-made disaster situations, and in many other settings. The workshop objective is to advance the state of the art of the science of UQ. The objective is met by bringing together mathematicians, statisticians, engineers, and scientists from universities and industry to exchange ideas and to develop new methodologies. A significant and effective transfer of knowledge to the users of scientific UQ is also affected. The organizers of the workshop are committed to include a diverse, with respect to rank, gender, age, and ethnicity, set of participants in the workshop. There is also a well-formulated plan for the timely and effective dissemination of information about developments occurring at the workshop. The workshop closes with a session devoted to a discussion of future directions in UQ research with a special emphasis on the outstanding open problems that need to be solved in order to make stochastic PDE-based UQ a tool that is easily, routinely, and readily available to those in government and industry that have to make decisions in environments involving risk and uncertainty.