The prediction of photon echoes is an important technique for gaining an
understanding of optical quantum systems. However, this requires a large number
of simulations with varying parameters and/or input pulses, which renders
numerical studies expensive. This article investigates how we can use
data-driven surrogate models based on the Koopman operator to accelerate this
process. In order to be successful, we require a model that is accurate over a
large number of time steps. To this end, we employ a bilinear Koopman model
using extended dynamic mode decomposition and simulate the optical Bloch
equations for an ensemble of inhomogeneously broadened two-level systems. Such
systems are well suited to describe the excitation of excitonic resonances in
semiconductor nanostructures, for example, ensembles of semiconductor quantum
dots. We perform a detailed study on the required number of system simulations
such that the resulting data-driven Koopman model is sufficiently accurate for
a wide range of parameter settings. We analyze the L2 error and the relative
error of the photon echo peak and investigate how the control positions relate
to the stabilization. After proper training, the dynamics of the quantum
ensemble can be predicted accurately and numerically very efficiently by our
methods