Abstract: The magnetic fields in stellarators can be organized into different regions according to the dynamics of field line flows, with regions of nested flux surfaces potentially interspersed with islands or regions of chaos. While can visualize these structures with Poincare plots, such visualizations are not wholly satisfactory if we wish to numerically optimize such structures. In this talk, we describe an approach to automatically inferring the structure of magnetic field line flows by building models of the dynamics of field line trajectories with connections to dynamical systems theory, numerical extrapolation methods, and the theory of adaptive filtering. Joint work with Max Ruth (UT Austin).