The explosive growth in the use of computer simulators in the last fifteen years has helped galvanize a revolution in scientific, engineering, and biological research that includes advances in the aerospace industry, material science, renewable energy, and biomechanics. Researchers can make a detailed exploration of scientific design alternatives under a wide set of operating environments using runs from a simulator of a physical system, possibly coupled with those from a traditional physical system experiment. This research project will advance the statistical modeling, design, and analysis of experiments that use computer simulators. The first research area is Improved Modeling of Simulator Output: The investigators will develop flexible stochastic models that will allow more accurate prediction in settings where the simulator provides related multivariate output of the performance of a physical system. Current prediction models either assume output independence (knowledge of one output gives no information about other outputs) or a linear dependence on a common set of latent drivers. The second research area concerns Advances in Emulation: The investigators aim to devise efficient emulators of simulator output for novel input and output settings such as when gradient information is available or when the output consists of both point and integrated measures. They plan to construct predictors that incorporate natural invariances present in the simulator output. For example, the predicted response should be constant under permutations of the inputs when the output satisfies this condition; the project will quantify the uncertainty in the invariant predictors. The investigators also plan to quantify the uncertainty of a recent, theoretically-justified method of calibrating computer simulators based on physical experimental data. The third research area is the Design of Simulator Experiments: Efficient designs of simulator experiments will be devised to minimize the computational effort required to determine the sensitivity of a simulator output to each of its inputs.
This research will build a statistical framework for the modeling, design and analysis of experiments that employ computer simulators. The specific goals are (1) to devise flexible interpolating stochastic models for computer simulators with multivariate output; (2) to invent efficient predictors for novel input and output settings such as when gradient information is available or when the output consists of both point and integrated responses; (3) to develop emulators of simulator output that incorporate the same invariances present in the simulator responses; (4) to quantify the uncertainty of L2 calibrated predictors for expensive computer codes; and (5) to construct new sliced Latin hypercube designs to allow the efficient calculation of global sensitivity indices. The investigators will develop new modes for training statistics graduate students having interests in engineering applications. Opportunities will be created for subject matter specialists to provide critical practical challenges in three areas: aerospace/mechanical engineering, biomechanics, and material science, and to conduct joint applied projects with the researchers.
