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