  While the interaction of ultra-intense ultra-short laser pulses with near-
and overcritical plasmas cannot be directly observed, experimentally accessible
quantities (observables) often only indirectly give information about the
underlying plasma dynamics. Furthermore, the information provided by
observables is incomplete, making the inverse problem highly ambiguous.
Therefore, in order to infer plasma dynamics as well as experimental parameter,
the full distribution over parameters given an observation needs to considered,
requiring that models are flexible and account for the information lost in the
forward process. Invertible Neural Networks (INNs) have been designed to
efficiently model both the forward and inverse process, providing the full
conditional posterior given a specific measurement. In this work, we benchmark
INNs and standard statistical methods on synthetic electron spectra. First, we
provide experimental results with respect to the acceptance rate, where our
results show increases in acceptance rates up to a factor of 10. Additionally,
we show that this increased acceptance rate also results in an increased
speed-up for INNs to the same extent. Lastly, we propose a composite algorithm
that utilizes INNs and promises low runtimes while preserving high accuracy.
