  The main goal is to construct a combinatorial dynamical system in the sense
of Forman from finite vector field data. We use a linear minimization problem
with binary variables and linear equality constraints. The solution of the
minimization problem induces an admissible matching for the combinatorial
dynamical system. They are three main steps for the method: Construct a
simplicial complex, compute a vector for each simplex, solve the minimization
problem, and apply the induced matching. We argue the effectiveness of the
method by testing it on the Lotka-Volterra model and the Lorenz attractor
model. We are able to retrieve the cyclic behaviour in the Lotka-Volterra model
and the chaotic behaviour of the Lorenz attractor. Two extensions to the
algorithm are shown. We use the barycentric subdivision to obtain a better
resolution. We add conditions on the minimization problem to obtain a solution
which induce a gradient matching.
