Detection of Multiband Lensed Gravitational Waves from Dark Matter Halos with Deep Learning

Lensed gravitational waves acquire amplitude and phase modulations when propagating through the gravitational potential of dark matter halos, producing interference structures in the observed waveform. However, these features are often difficult to identify in detector noise. In this work, we develop a deep learning framework for the automatic classification of lensed gravitational wave signals under multiband observations. We simulate binary neutron star signals observed by the space based detector DECIGO and the ground based Einstein Telescope, and construct five classes of data including pure noise, unlensed signals, and three lensed cases generated by the SIS, CIS, and NFW dark matter halo models. By comparing single detector and joint detector configurations, we evaluate the classification performance under different observational settings. The results show that multiband observations significantly improve the identification of lensed signals and reduce confusion among different lens models. This approach provides an efficient method for automated recognition of lensed gravitational waves in future multiband gravitational wave observations.