  The multi-messenger astrophysics of compact objects presents a vast range of
environments where neutrino flavor transformation may occur and may be
important for nucleosynthesis, dynamics, and a detected neutrino signal.
Development of efficient techniques for surveying flavor evolution solution
spaces in these diverse environments, which augment and complement existing
sophisticated computational tools, could leverage progress in this field. To
this end we continue our exploration of statistical data assimilation (SDA) to
identify solutions to a small-scale model of neutrino flavor transformation.
SDA is a machine learning (ML) formula wherein a dynamical model is assumed to
generate any measured quantities. Specifically, we use an optimization
formulation of SDA wherein a cost function is extremized via the variational
method. Regions of state space in which the extremization identifies the global
minimum of the cost function will correspond to parameter regimes in which a
model solution can exist. Our example study seeks to infer the flavor
transformation histories of two mono-energetic neutrino beams coherently
interacting with each other and with a matter background. We require that the
solution be consistent with measured neutrino flavor fluxes at the point of
detection, and with constraints placed upon the flavor content at various
locations along their trajectories, such as the point of emission, and the
locations of the Mikheyev-Smirnov-Wolfenstein (MSW) resonances. We show how the
procedure efficiently identifies solution regimes and rules out regimes where
solutions are infeasible. Overall, results intimate the promise of this
"variational annealing" methodology to efficiently probe an array of
fundamental questions that traditional numerical simulation codes render
difficult to access.
