  We propose an experimental scheme for performing sensitive, high-precision
laser spectroscopy studies on fast exotic isotopes. By inducing a step-wise
resonant ionization of the atoms travelling inside an electric field and
subsequently detecting the ion and the corresponding electron, time- and
position-sensitive measurements of the resulting particles can be performed.
Using a Mixture Density Network (MDN), we can leverage this information to
predict the initial energy of individual atoms and thus apply a Doppler
correction of the observed transition frequencies on an event-by-event basis.
We conduct numerical simulations of the proposed experimental scheme and show
that kHz-level uncertainties can be achieved for ion beams produced at extreme
temperatures ($> 10^8$ K), with energy spreads as large as $10$ keV and
non-uniform velocity distributions. The ability to perform in-flight
spectroscopy, directly on highly energetic beams, offers unique opportunities
to studying short-lived isotopes with lifetimes in the millisecond range and
below, produced in low quantities, in hot and highly contaminated environments,
without the need for cooling techniques. Such species are of marked interest
for nuclear structure, astrophysics, and new physics searches.
