The breaking of ergodicity in isolated quantum systems with a single-particle mobility edge is an intriguing subject that has not yet been fully understood. In particular, whether a nonergodic but metallic phase exists or not in the presence of a one-dimensional quasi-periodic potential is currently under active debate. In this talk, I will discuss how to use a neural-network based approach to investigate the existence of this nonergodic metallic phase using many-body entanglement spectra as the sole diagnostic. Such a method identifies with high confidence the existence of a nonergodic metallic phase in the mid spectrum at an intermediate quasiperiodic potential strength. Our method shows how supervised machine learning can be applied not only in locating phase boundaries, but also in providing a way to definitively examine the existence or not of a novel phase.