Bright, short-pulsed neutron beams from laser-driven neutron sources (LANSs) provide a new perspective on material screening via fast neutron activation analysis (FNAA). FNAA is a nondestructive technique for determining material elemental composition based on nuclear excitation by fast neutron bombardment and subsequent spectral analysis of prompt γ-rays emitted by the active nuclei. Our recent experiments and simulations have shown that activation analysis can be used in practice with modest neutron fluences on the order of 105 n/cm2, which is available with current laser technology. In addition, time-resolved γ-ray measurements combined with picosecond neutron probes from LANSs are effective in mitigating the issue of spectral interference between elements, enabling highly accurate screening of complex samples containing many elements. This paper describes the predictive capability of LANS-based activation analysis based on experimental demonstrations and spectral calculations with Monte Carlo simulations.