Efficient Identification of Promising Regions in High-Dimensional Design Spaces With Multilevel Materials Design Applications

Abstract

Design space exploration can reveal the underlying structure of design problems of interest. In a set-based approach, for example, exploration can identify sets of designs or regions of the design space that meet specific performance requirements. For some problems, promising designs may cluster in multiple regions of the design space, and the boundaries of those clusters may be irregularly shaped and difficult to predict. Visualizing the promising regions can clarify the design space structure, but design spaces are typically high-dimensional, making it difficult to visualize the space in three dimensions. Techniques have been introduced to map high-dimensional design spaces to low-dimensional, visualizable spaces. Before the promising regions can be visualized, however, the first task is to identify how many clusters of promising designs exist in the high-dimensional design space. Unsupervised machine learning methods, such as spectral clustering, have been utilized for this task. Spectral clustering is generally accurate but becomes computationally intractable with large sets of candidate designs. Therefore, in this paper a technique for accurately identifying clusters of promising designs is introduced that remains viable with large sets of designs. The technique is based on spectral clustering but reduces its computational impact by leveraging the Nyström Method in the formulation of self-tuning spectral clustering. After validating the method on a simplified example, it is applied to identify clusters of high performance designs for a high-dimensional negative stiffness metamaterials design problem.