Generalized tessellation based design and analysis of computer experiments with manifold input spaces
This research seeks to develop a general methodology for design and optimization of computer experiments called a generalized tessellation based design (GTD). The method is designed for input spaces that are connected smooth manifolds. There exist many methods for designing computer experiments, but many of these methods are either too rigid in the assumptions made, cannot handle constrained input spaces such as some manifolds, or simply lack the ability to adapt to certain types of problems. GTD rectifies these shortcomings. The method tessellates the input space based on Dirichlet or Voronoi cells generated by previously sampled points. Then new points are selected by sampling from within the Voronoi cell having a maximum measure defined by an area relative to a prior density or other objective function. Lastly, new sample points are selected according to a local placement criteria defined by the analyst. Theoretical properties of the GTD methodology are shown. These include the convergence of GTD for optimization and the representation of the prior density in GTD for experimental design. Furthermore, examples of GTD used for experimental design and for optimizing function is presented with favorable results. Lastly an application to a 22 dimensional nonlinear differential equation model of glucose kinetics is shown and compared against other methods for calibrating the simulation to data.