  We assess the utility of an optimization-based data assimilation (D.A.)
technique for treating the problem of nonlinear neutrino flavor transformation
in core collapse supernovae. D.A. uses measurements obtained from a physical
system to estimate the state variable evolution and parameter values of the
associated model. Formulated as an optimization procedure, D.A. can offer an
integration-blind approach to predicting model evolution, which offers an
advantage for models that thwart solution via traditional numerical integration
techniques. Further, D.A. performs most optimally for models whose equations of
motion are nonlinearly coupled. In this exploratory work, we consider a simple
steady-state model with two mono-energetic neutrino beams coherently
interacting with each other and a background medium. As this model can be
solved via numerical integration, we have an independent consistency check for
D.A. solutions. We find that the procedure can capture key features of flavor
evolution over the entire trajectory, even given measurements of neutrino
flavor only at the endpoint, and with an assumed known initial flavor
distribution. Further, the procedure permits an examination of the sensitivity
of flavor evolution to estimates of unknown model parameters, locates
degeneracies in parameter space, and can identify the specific measurements
required to break those degeneracies.
