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

Abstract

Computer models and simulations are essential system design tools that allow for improved decision making and cost reductions during all phases of the design process. However, the most accurate models tend to be computationally expensive and can therefore only be used sporadically. Consequently, designers are often forced to choose between exploring many design alternatives with less accurate, inexpensive models and evaluating fewer alternatives with the most accurate models. To achieve both broad exploration of the design space and accurate determination of the best alternatives, surrogate modeling and variable accuracy modeling are gaining in popularity. A surrogate model is a mathematically tractable approximation of a more expensive model based on a limited sampling of that model. Variable accuracy modeling involves a collection of different models of the same system with different accuracies and computational costs. We hypothesize that designers can determine the best solutions more efficiently using surrogate and variable accuracy models. This hypothesis is based on the observation that very poor solutions can be eliminated inexpensively by using only less accurate models. The most accurate models are then reserved for discerning the best solution from the set of good solutions. In this paper, a new approach for global optimization is introduced, which uses variable accuracy models in conjuction with a kriging surrogate model and a sequential sampling strategy based on a Value of Information (VOI) metric. There are two main contributions. The first is a novel surrogate modeling method that accommodates 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. However, in this new approach, the error between the model output and the unknown truth (the real world process) is explicitly accounted for. When variable accuracy data is used, the resulting response surface does not interpolate the data points but provides an approximate fit giving the most weight to the most accurate data. The second contribution is a new method for sequential sampling. Information from the current surrogate model is combined with the underlying variable accuracy models’ cost and accuracy to determine where best to sample next using the VOI metric. This metric is used to mathematically determine where next to sample and with which model. In this manner, the cost of further analysis is explicitly taken into account during the optimization process.