The Woodruff School

SUMMARY

As computational models and simulations improve in quality, the cost of evaluating sophisticated models is increasing. In spite of the advancements in computing technology, many very accurate models in the engineering and science domains have long processing times. As a result, the use of surrogate models and variable accuracy models has become prevalent in systems design problems. A surrogate model is a mathematically tractable approximation of a more expensive model, based on a limited sampling of that model. Similarly, variable accuracy models are a collection of different models of the same system but with different levels of accuracy and different computational costs. The use of such models allows designers to achieve a good solution at reasonable cost, but often this cost is not directly accounted for in the overall utility of the final product. In this proposal, a novel surrogate modeling method is presented for accommodating data from any number of different models of varying accuracy and cost. The proposed surrogate model is Gaussian process-based, much like classic kriging modeling approaches. Classic kriging is an interpolation technique that inherently assumes zero error at the design sites; this is logical because most computer experiments are deterministic. However, by relaxing this assumption, the deviation between the model output and the physical truth is formally recognized. While the truth is generally not known in practice, the quality of a model can be characterized based on average error with respect to the truth. Using this novel surrogate modeling approach, a new optimization method is presented. Information from the surrogate model is combined with model cost and accuracy data in the Value of Information (VOI) metric. This metric, based on the current knowledge state and best sampled point, mathematically determines where next to sample and with what degree of model accuracy. In this manner, the cost of further analysis is formally taken into account during the optimization process.

SUBJECT:	Ph.D. Proposal Presentation

BY:	Roxanne Moore

TIME:	Friday, November 12, 2010, 1:00 p.m.

PLACE:	MRDC Building, 4211

TITLE:	A Rational Design Approach to Gaussian Process Modeling for Variable Fidelity Models

COMMITTEE:	Dr. Chris Paredis, Chair (ME) Dr. Bert Bras (ME) Dr. Jeff Wu (ISYE) Dr. Michael Leamy (ME) Dr. David Romero (Universidad del Zulia)

SUMMARY As computational models and simulations improve in quality, the cost of evaluating sophisticated models is increasing. In spite of the advancements in computing technology, many very accurate models in the engineering and science domains have long processing times. As a result, the use of surrogate models and variable accuracy models has become prevalent in systems design problems. A surrogate model is a mathematically tractable approximation of a more expensive model, based on a limited sampling of that model. Similarly, variable accuracy models are a collection of different models of the same system but with different levels of accuracy and different computational costs. The use of such models allows designers to achieve a good solution at reasonable cost, but often this cost is not directly accounted for in the overall utility of the final product. In this proposal, a novel surrogate modeling method is presented for accommodating data from any number of different models of varying accuracy and cost. The proposed surrogate model is Gaussian process-based, much like classic kriging modeling approaches. Classic kriging is an interpolation technique that inherently assumes zero error at the design sites; this is logical because most computer experiments are deterministic. However, by relaxing this assumption, the deviation between the model output and the physical truth is formally recognized. While the truth is generally not known in practice, the quality of a model can be characterized based on average error with respect to the truth. Using this novel surrogate modeling approach, a new optimization method is presented. Information from the surrogate model is combined with model cost and accuracy data in the Value of Information (VOI) metric. This metric, based on the current knowledge state and best sampled point, mathematically determines where next to sample and with what degree of model accuracy. In this manner, the cost of further analysis is formally taken into account during the optimization process.