The atomistic modeling of amorphous materials requires structure sizes and sampling statistics that are challenging to achieve with first-principles methods. Here, we propose a methodology to speed up the sampling of amorphous and disordered materials using a combination of a genetic algorithm and a specialized machine-learning potential based on artificial neural networks (ANN)... We show for the example of the amorphous LiSi alloy that around 1,000 first-principles calculations are sufficient for the ANN potential assisted sampling of low-energy atomic configurations in the entire amorphous LixSi phase space. The obtained phase diagram is validated by comparison with the results from an extensive sampling of LixSi configurations using molecular dynamics simulations and a general ANN potential trained to ~45,000 first-principles calculations. This demonstrates the utility of the approach for the first-principles modeling of amorphous materials. (read more)