Capacitive micromechanical ultrasonic transducers (CMUTs), as microelectromechanical systems (MEMS) devices, have broad application prospects in ultrasonic imaging and sensing. This study investigates the influence of surface acoustic waves (SAWs) using periodically arranged CMUTs as the fundamental unit cells. We first utilize finite element analysis (FEA) to calculate and analyze the band structure and bandgap characteristics of phononic crystals under infinite periodic conditions. Subsequently, for finite periodic structures in practical applications, acoustic transmission spectra were further simulated using FEA to verify the bandgap characteristics of the structure for SAWs. Accordingly, this paper leverages a deep learning framework based on a multilayer perceptron (MLP) architecture to achieve the inverse design and optimization of CMUT geometric parameters, tailored to specific target bandgap requirements. The results demonstrate that this approach can efficiently and accurately determine the optimal structural configurations, offering a robust and novel technical paradigm for the precise control of SAWs using CMUT-based periodic arrays.