Decision Making Under Uncertainty: Assessment of the Reliability of Mathematical Models

Mathematical modeling, particularly in the form of numerical simulation, has become increasingly important in engineering and industrial applications. The ability to model and predict behavior of systems has allowed engineers to design products without building prototypes, and therefore shortening the length of the design cycle. The approach has the added advantage that it reduces the cost of a design process, while allowing the engineer to explore many designs in a short time span.

While there are a number of successful products that have been designed with the aid of mathematical modeling, what is less clear is the extent to which a designer can rely on a mathematical model. There are several sources of uncertainty in a numerical simulation. For example the parameters entering a given model, such as geometrical description, material properties, excitations, are usually known only up to some level of accuracy. Moreover, there are situations when parameters in a problem of interest are beyond the range in which we can "trust" a mathematical model. Many computer simulations are approximate solutions to an underlying continuous system. While we often can validate an approximate solution for a given problem by comparing the output with carefully obtained experimental data, there are clear limitations to the discretization level in the approximation, and hence the ultimate accuracy of a simulation. These factors suggest that most numerical simulations must be used carefully in any decision process, and that uncertainty in the simulations can be introduced by a variety of sources.

This workshop has been organized to address the question of how to assess the reliability of a mathematical model. The participants will be researchers from academia and industry with expertise in numerical analysis and scientific computing, experimental validation, applied statistics. It is meant to provide a forum for discussion of sources of uncertainty, and ways of assessing their impact on a numerical model. The workshop will bring leading researchers who have made contribution to the understanding of uncertainty in several areas of application.

Topics that will be addressed in this workshop are:

• Sources of uncertainty
• Sensitivity analysis
• Stability and robustness
• Experimental validation
• Statistical analysis of computer experiments
• A posteori error estimation

The goal of the workshop is to produce a document which articulates the problems arising in the assessment of uncertainty, and set research directions. It is hoped that future research will result in methods and procedures for quantitative assessment of reliability of mathematical models.