In some design domains, particularly rapidly evolving domains such as tissue engineering, analytical representations of the system do not exist. In these domains, the design process can be facilitated by the development of surrogate models that provide an understanding of the interactions of parameters and their influence on system performance, even though the models do not explain the underlying phenomena. Often, physical experiments are the only method for obtaining information about such systems. In particular, in bioengineering design domains, experiments are expensive and must be replicated to account for biological variability. Surrogate models can reduce the number of experiments needed and increase the value of the information gained through experimentation. In this paper, we present a framework for incorporating information from replications (repeated experiments) into Bayesian surrogate models. Within this framework, we develop uncertainty measurements for the prediction of the surrogate model. We illustrate the framework with two test cases using analytical functions. We then present a biomedical example used in the design of scaffold materials for the regeneration of bone tissue to show the use of Bayesian surrogates in exploratory design.

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