A minimal-data approach for spatially resolved parameter analysis of coupled graphene nanomechanical resonators

Networks of nanoelectromechanical (NEMS) resonators are useful analogs for a variety of many-body systems and enable applications in sensing, phononics, and mechanical information processing. A challenge toward realizing practical NEMS networks is the ability to characterize the constituent resonator building blocks and their coupling. Here, we spatially map graphene NEMS networks and introduce an efficient algebraic formalism to quantify the site-specific elasticity, mass, damping, and coupling parameters of network clusters. In a departure from multiple regression, our algebraic analysis uses minimal measurements to fully characterize the network parameters without a priori parameter estimates or iterative computation. We apply this suite of techniques to single-resonator and coupled-pair clusters and find excellent agreement with expected parameter values and broader spectral response. Our approach provides a nonregressive framework for accurately characterizing a range of classical and quantum resonator systems, offering a versatile modeling tool applicable across multiple disciplines and advancing the development of programmable NEMS networks.