  Understanding neutrino flavor transformation in dense environments such as
core-collapse supernovae (CCSN) is critical for inferring nucleosynthesis and
interpreting a detected neutrino signal. The role of direction-changing
collisions in shaping the neutrino flavor field in these environments is
important and poorly understood; it has not been treated self-consistently.
There has been progress, via numerical integration, to include the effects of
collisions in the dynamics of the neutrino flavor field. While this has led to
important insights, integration is limited by its requirement that full initial
conditions must be assumed known. On the contrary, feedback from collisions to
the neutrino field is a boundary value problem. Numerical integration
techniques are poorly equipped to handle that formulation. This paper
demonstrates that an inference formulation of the problem can solve a simple
collision-only model representing a CCSN core -- without full knowledge of
initial conditions. Rather, the procedure solves a two-point boundary value
problem with partial information at the bounds. The model is sufficiently
simple that physical reasoning may be used as a confidence check on the
inference-based solution, and the procedure recovers the expected model
dynamics. This result demonstrates that inference can solve a problem that is
artificially hidden from integration techniques -- a problem that is an
important feature of flavor evolution in dense environments. Thus, it is
worthwhile to explore means of augmenting the existing powerful integration
tools with inference-based approaches.
