The inverse problem of broadband amplification is very important in research on the properties of laser amplifier. Analytic electric polarization in the temporal domain is applied to broadband amplification in the sub-nanosecond time scale. The inverse problem of broadband amplification is studied and simulated numerically in detail by use of genetic algorithm and Gerchberg-Saxton (GS) algorithm, namely, to solve the input pulsed-laser spatial and temporal shape from the given output pulsed-laser and laser amplifier parameters. On one hand, analytic electric polarization in the temporal domain is more effective to solve broadband amplification, on the other hand hybrid intelligent algorithm greatly simplifies the inverse-problem modeling of broadband amplification, and accelerates the convergence of the solution to inverse problem.