A structure consisting of a perforated plate backed by an air cavity is a widely used structure for sound absorption in the low-to-high frequency range. In this study, we propose a sound absorbing metastructure composed of a polydimethylsiloxane (PDMS)-based flexible perforated plate backed by a layer of multiple hexagonal unit cells. Each unit cell consists of a dual cavity connected by a rigid perforated plate. The proposed structure allows for enhanced vibroacoustic coupling between the perforated plate and the back cavity. First, the structure is theoretically simulated using the finite element based analysis. The results elicit that the shape and size of the back cavity significantly alter the sound absorption coefficient and the resonant frequency of the structure. The geometrical parameters of the metastructure were further optimized using an artificial intelligence-based technique. Using the optimized geometrical parameters, the back cavity was printed using selective laser sintering (SLS) and a PDMS perforated plate has adhered on top of it. The experimental results demonstrate a potential sound absorption metastructure which can be utilized for multiple applications.