Surrogate Models

A surrogate model can be roughly thought of as a mathematical "curve fit" through a set of data generated by your analysis code. In Design Explorer, surrogate models serve as substitutes for potentially expensive and "noisy" computer simulations. The smooth and inexpensive-to-evaluate surrogate models make the global analysis and optimization processes tractable.

To create a surrogate model, Design Explorer executes your analysis code (Analyzer model) multiple times, and stores the results of each run in a table. The input variable values for this series of runs are chosen to efficiently canvas the design space (using an Orthogonal Array). The data generated by your analysis code is then used to construct the surrogate models - one for each objective and each constraint in your design problem.

The surrogate models used by Design Explorer (DACE models) are interpolating Kriging models [1]. Roughly speaking, a Design Explorer response model is chosen from a class of models flexible enough to represent complexity in the responses without imposing a restrictive model form as in, for example, a least squares fit to a quadratic model. The models provide an effective approach for exploring the design space globally, for understanding the important variables in a problem, and for reducing the dimension of an optimization problem.

A key feature of the surrogate models used in Design Explorer is their ability to be efficiently recalibrated as new data becomes available [2]. The figure below contrasts least squares quadratic fits and DACE fits before and after calibrating with additional samples.

References

[1] Booker, A. J., "Design and Analysis of Computer Experiments," 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, St. Louis, MO, (Sept. 2-4, 1998) pp. 118-128. AIAA-98-4757.

[2] Audet, C., Dennis, J.E., Moore, D.W., Booker, A.J., and Frank P.D., "A Surrogate-Model-Based Method for Constrained Optimization," 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Long Beach, CA, (September 8, 2000) AIAA-2000-4891.