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

From Finite Vector Field Data to Combinatorial Dynamical Systems in the Sense of Forman