Simon Mak

Minimax and Minimax Projection Designs Using Clustering

ABSTRACT Minimax designs provide a uniform coverage of a design space by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful applications, for example, for optimal sensor allocation or as space-filling designs for computer experiments, there has been little work in developing algorithms for generating these designs, due to its computational complexity. In this article, a new hybrid algorithm combining particle swarm optimization and clustering is proposed for generating minimax designs on any convex and bounded design space. The computation time of this algorithm scales linearly in dimension p, meaning our method can generate minimax designs efficiently for high-dimensional regions. Simulation studies and a real-world example show that the proposed algorithm provides improved minimax performance over existing methods on a variety of design spaces. Finally, we introduce a new type of experimental design called a minimax projection design, and show that this proposed design provides better minimax performance on projected subspaces of compared to existing designs. An efficient implementation of these algorithms can be found in the R package minimaxdesign. Supplementary material for this article is available online.

cmenet: A New Method for Bi-Level Variable Selection of Conditional Main Effects

ABSTRACT This article introduces a novel method for selecting main effects and a set of reparameterized effects called conditional main effects (CMEs), which capture the conditional effect of a factor at a fixed level of another factor. CMEs represent interpretable, domain-specific phenomena for a wide range of applications in engineering, social sciences, and genomics. The key challenge is in incorporating the implicit grouped structure of CMEs within the variable selection procedure itself. We propose a new method, cmenet, which employs two principles called CME coupling and CME reduction to effectively navigate the selection algorithm. Simulation studies demonstrate the improved CME selection performance of cmenet over more generic selection methods. Applied to a gene association study on fly wing shape, cmenet not only yields more parsimonious models and improved predictive performance over standard two-factor interaction analysis methods, but also reveals important insights on gene activation behavior, which can be used to guide further experiments. Efficient implementations of our algorithms are available in the R package cmenet in CRAN. Supplementary materials for this article are available online.

An Efficient Surrogate Model for Emulation and Physics Extraction of Large Eddy Simulations

ABSTRACT In the quest for advanced propulsion and power-generation systems, high-fidelity simulations are too computationally expensive to survey the desired design space, and a new design methodology is needed that combines engineering physics, computer simulations, and statistical modeling. In this article, we propose a new surrogate model that provides efficient prediction and uncertainty quantification of turbulent flows in swirl injectors with varying geometries, devices commonly used in many engineering applications. The novelty of the proposed method lies in the incorporation of known physical properties of the fluid flow as simplifying assumptions for the statistical model. In view of the massive simulation data at hand, which is on the order of hundreds of gigabytes, these assumptions allow for accurate flow predictions in around an hour of computation time. To contrast, existing flow emulators which forgo such simplifications may require more computation time for training and prediction than is needed for conducting the simulation itself. Moreover, by accounting for coupling mechanisms between flow variables, the proposed model can jointly reduce prediction uncertainty and extract useful flow physics, which can then be used to guide further investigations. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.