  In the most extreme astrophysical environments, such as core-collapse
supernovae (CCSNe) and neutron star mergers (NSMs), neutrinos can undergo fast
flavor conversions (FFCs) on exceedingly short scales. Intensive simulations
have demonstrated that FFCs can attain equilibrium states in certain models. In
this study, we utilize physics-informed neural networks (PINNs) to predict the
asymptotic outcomes of FFCs, by specifically targeting the first two moments of
neutrino angular distributions. This makes our approach suitable for
state-of-the-art CCSN and NSM simulations. Through effective feature
engineering and the incorporation of customized loss functions that penalize
discrepancies in the predicted total number of $\nu_e$ and $\bar\nu_e$, our
PINNs demonstrate remarkable accuracies, with an error margin of $\lesssim3\%$.
Our study represents a substantial leap forward in the potential incorporation
of FFCs into simulations of CCSNe and NSMs, thereby enhancing our understanding
of these extraordinary astrophysical events.
