  Data-driven methods of model identification are able to discern governing
dynamics of a system from data. Such methods are well suited to help us learn
about systems with unpredictable evolution or systems with ambiguous governing
dynamics given our current understanding. Many plasma problems of interest fall
into these categories as there are a wide range of models that exist, however
each model is only useful in a certain regime and often limited by
computational complexity. To ensure data-driven methods align with theory, they
must be consistent and predictable when acting on data whose governing dynamics
are known. Weak Sparse Identification of Nonlinear Dynamics (WSINDy) is a
recently developed data-driven method that has shown promise in learning
governing dynamics from data with high noise levels [1]. This work examines how
WSINDy acts on ideal MHD test problems as the initial conditions are varied and
specifies limiting requirements for successful equation identification. It is
hard to recover the governing dynamics from data that emphasize a single
dominant behavior. In these low information cases, Shannon information entropy
is able to pick up on the redundancies in the data that affect recoverability.
