Quantifying Uncertainty: SIAM Workshop Targets Promising Research Areas

December 16, 1998

The standing-room-only Toronto minisymposium on uncertainty and predictability described by Barry Cipra in the accompanying article grew out of a SIAM workshop held just about a month earlier, June 12-13, 1998, at the National Science Foundation.

SIAM conducted the workshop, "Uncertainty Management and Assessment," in response to a request from Donald J. Lewis, director of the Division of Mathematical Sciences at NSF. Since his arrival at NSF more than three years ago, Lewis says, he has been encouraging the mathematics societies to hold workshops and sessions on developing opportunities in mathematics-of which he sees the science of uncertainty as an excellent example.

The approximately 20 participants in the two-day SIAM workshop, representing academia, industry, government agencies, and SIAM, met to clarify the growing importance of uncertainty in mathematical modeling and simulation, to highlight central difficulties in quantifying uncertainty, to identify critical areas for future research, and to recommend ways to nurture that research. John Guckenheimer, president of SIAM, chaired the workshop.

A report summarizing the results of the workshop is in the final stages of preparation as this issue of SIAM News goes to press. The report discusses a number of important application areas that require a better understanding of uncertainty, such as global climate modeling and integrated design of complex systems.

The report considers how various sources of uncertainty, including inaccurate or approximate models, incomplete or inaccurate data, discretization and numerical errors, all interact with each other and propagate through complex models in ways that are not easily quantifiable. This becomes particularly troublesome in large complex systems with many heterogeneous components-continuous and discrete, stochastic and deterministic-on multiple scales.

"A popular myth that is very ingrained in our technical culture," says workshop participant John Doyle of Caltech, "is that the problem of uncertainty due to unmodeled dynamics is adequately handled by simply increasing the resolution of the model until all the relevant phenomena are included." The report argues for the need to understand and, to the extent possible, to explicitly represent and quantify all sources of uncertainty in models and simulation.

The report takes as its starting point the assumption that modeling, computational simulation, and data analysis are essential to modern industry as well as to science itself. Areas in which these tools are needed include economic policy decision analysis, financial planning, military training, and the management of complex networks like electric power grids and various types of industrial design, from VLSI process design to integrated aircraft design.

As the report points out, methods are needed both for representing and quantifying uncertainty in computational simulations and for managing uncertainty.

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