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This paper summarizes the discussion at the Approximation Methods Panel that was held at the 9 ^th AIAA/ISSMO Symposium on Multidisciplinary Analysis & Optimization in Atlanta, GA on September 2–4, 2002. The objective of the panel was to discuss the current state-of-the-art of approximation methods and identify future research directions important to the community. The panel consisted of five representatives from industry and government: (1) Andrew J. Booker from The Boeing Company, (2) Dipankar Ghosh from Vanderplaats Research & Development, (3) Anthony A. Giunta from Sandia National Laboratories, (4) Patrick N. Koch from Engineous Software, Inc., and (5) Ren-Jye Yang from Ford Motor Company. Each panelist was asked to (i) give one or two brief examples of typical uses of approximation methods by his company, (ii) describe the current state-of-the-art of these …