Metamaterial perfect absorbers (MPAs) with high absorption, thin thickness, and custom-tailorable spectrum are in great demand in many applications, especially in photoelectric detectors. Presently, infrared (IR) focal plane array detectors based on type-II superlattice (T2SL) still face the challenge of a low absorption coefficient. Moreover, it is still difficult to integrate conventional metal-insulator-metal (MIM) MPA with a T2SL infrared detector, due to the incompatibility of fabrication processes. In addition, the need to achieve custom-tailorable multi-peak absorption in the long-wave infrared band is high, and the design process of an MPA with a complicated geometric shape is time-consuming. To tackle these problems, in this work, we replace the ground metal layer in a conventional MIM MPA with a heavily doped semiconductor (n++), whose growth process is compatible with the fabrication process of T2SL infrared detectors and thus can be integrated with them. Moreover, we set up a deep neural network (DNN) to associate the spectral response of the device with the corresponding structural parameters. In this way, we can quickly inverse design the infrared perfect absorber with multiple absorption peaks using a trained DNN. The designed devices can achieve three perfect absorption peaks in the wavelength range of interest (8 ∼ 13 µm), and the peak absorptivity generally reaches over 90%. Our work provides an effective method for the inverse design of n++IM MPA based on DNN, which is of significant guidance for the study of infrared MPA. Additionally, our work anticipates enhancing the detection performance of infrared detectors through absorption enhancement, indicating substantial application potential in the field of optically modulated infrared detectors.