A theoretical framework is presented for studying the existence of topological states at the interface between two stubbed mesoscopic crystals (MCs). This study is based on the recently proposed novel mechanism based on band edge symmetry inversion around a flat band, i.e., when the width of the passband vanishes, while using only one stub per unit cell. The theoretical investigation of these states involves various approaches, including analyzing the topology of the bands based on the Zak phase and the symmetry of the band edge modes. Additionally, we consider the sign of the reflection phase between each MC and a waveguide to predict the existence and the position of such interface state. Subsequently, A straightforward deep learning network is proposed for inversely engineering such states with desired topological properties. This approach encodes the desired Zak phase of the bulk crystal in the sign of reflection phase, allowing the model to predict the corresponding geometry. Remarkably, our model achieves a 97.13% accuracy in performing such tasks on un-seen data.