Speaker: Steven Bergner, SFU
Title: Point lattices with a fine-grained nesting property as experimental designs for multi-fidelity computer codes (Slides)
Abstract: Computer models that approximate the mean response in physical systems are often used in place of, or in addition to, experiments on the process of interest. In addition, there are often more than one computer model that can be used to represent the physical system ¨C each with different degrees of fidelity. This is the case in our application of radiative shock hydrodynamics where 1D and 2D simulation models are available to approximate the mean of the system over an experimental domain. The latter code provides more accurate calculations of the shock location and its breakout time, but requires orders of magnitude more running time than the former version. Fitting a Gaussian process model in this setting, allows us to obtain response estimates that take information from all codes into account.
It is known that a good experimental design (choice of parameter configuration points at which to run the codes) should have good space-filling properties (e.g. large packing or small covering radii of the point set). Beyond that, I argue for an additional nesting property, which allows the high-fidelity code to be run with a smaller design that is contained in the denser design for the low-fidelity one.
To address these requirements, I present a novel type of designs, namely point lattices that contain rotated and scaled versions of themselves. Different levels of resolution share a single type of Voronoi polytope, whose volume grows independently of the dimensionality by a chosen integer factor as low as 2. While this readily provides a fine-grained nesting property, I will also discuss how to optimize space-filling criteria and obtain multi-resolution lattice designs for arbitrary run sizes.