A Spectral Approach for the Design of Experiments: Design, Analysis and Algorithms
This work addresses the challenge of designing efficient experiments for applications such as optimization and simulation, offering a new analytic and computational framework that improves performance in high-dimensional settings.
The paper tackles the problem of constructing high-quality space-filling sample designs by proposing a novel metric to trade-off uniformity and randomness, connecting it to spectral analysis, and developing an optimization framework. The result shows that the proposed spectral designs significantly outperform existing approaches, particularly in high dimensions (2 to 6), as demonstrated in applications like image reconstruction and surrogate modeling.
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatial domain) to the objective measure of the design performance (defined in the spectral domain). This connection serves as an analytic framework for evaluating the qualitative properties of space-filling designs in general. Using the theoretical insights provided by this spatial-spectral analysis, we derive the notion of optimal space-filling designs, which we refer to as space-filling spectral designs. Third, we propose an efficient estimator to evaluate the space-filling properties of sample designs in arbitrary dimensions and use it to develop an optimization framework to generate high quality space-filling designs. Finally, we carry out a detailed performance comparison on two different applications in 2 to 6 dimensions: a) image reconstruction and b) surrogate modeling on several benchmark optimization functions and an inertial confinement fusion (ICF) simulation code. We demonstrate that the propose spectral designs significantly outperform existing approaches especially in high dimensions.