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Given the damages from earthquakes, seismic isolation of criticalinfrastructure is vital to mitigate losses due to seismic events. A promisingapproach for seismic isolation systems is metamaterials-based wave barriers.Metamaterials -- engineered composites -- manipulate the propagation andattenuation of seismic waves. Borrowing ideas from phononic and sonic crystals,the central goal of a metamaterials-based wave barrier is to create band gapsthat cover the frequencies of seismic waves. The two quantities of interest(QoIs) that characterize band-gaps are the first-frequency cutoff and theband-gap's width. Researchers often use analytical (band-gap analysis),experimental (shake table tests), and statistical (global variance) approachesto tailor the QoIs. However, these approaches are expensive andcompute-intensive. So, a pressing need exists for alternative easy-to-usemethods to quantify the correlation between input (design) parameters and QoIs.To quantify such a correlation, in this paper, we will use Shapley values, atechnique from the cooperative game theory. In addition, we will developmachine learning models that can predict the QoIs for a given set of input(material and geometrical) parameters.

Shapley values and machine learning to characterize metamaterials for seismic applications