Complex Experiments and High-Input Simulators: Challenges in Design, Prediction and Sensitivity

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The investigators study five problem areas. (1) A primary objective is to provide designs that have high predictive efficiency over a wide class of objective functions for simulator-only and simulator+physical experiments. Experimental designs will be constructed based on a new Bayesian prediction criterion. (2) The researchers will formulate regularization priors for use with simulators that require large numbers of inputs and are sampled sparsely. In particular, regularization priors will be developed for regression coefficients in the mean structure for non-stationary GP models as well as new priors to regularize the parameters controlling the correlation function. (3) Batch sequential design and analysis methodology will be developed to determine settings of control variables for minimizing the mean and variability of the response in the presence of non-controllable environmental variables. (4) The investigators will develop methods for determining the sensitivity of simulator outputs to inputs in mixed quantitative-qualitative variable settings, including non-rectangular input applications. (5) Methodology will be devised for constructing space-filling designs for computer codes with high-dimensional, non-rectangular regions whose boundaries can only be determined numerically. For example, computational models of long-scale temporal phenomena such as climate and galaxy formation models, have inputs regions are only partially known a priori.The complex physical and biological processes required to provide advances in many engineering and scientific fields are increasinglystudied using deterministic computer simulators coded from physics- or biology-based mathematical models. In many such applications, the data from related physical experiments are also available. The goals in such studies range from optimizing system performance in a given environment to designing systems that perform well in a wide variety of environments. The investigators are conducting research on efficient methods for determining input combinations at which to run complex simulator codes and associated physical experiments. They are also developing methods to extract the maximum information about the relevant engineering and scientific questions from such combined experiments. Techniques and results developed by the investigators are used in the specific collaborative projects in which the investigators participate. These include the following applications: (a) Tissue engineering where stress-strain simulators form part of the process of designing specialty tissues such as meniscal substitutes which are meant to perform well in a patient population; (b) Design of coating systems to extend the life of machine tools in tribological and wear applications; (c) Decreasing the shrinkage in injection molding applications; (d) Prediction of climate and weather based on detailed circulation computer models ofthe atmosphere.