Abstract: In this talk, I, first, will provide some preliminary definitions and observations on Dirac/big-isotropic structures and Hamiltonian inverse problem. Then I will present an algorithm to solve the Hamiltonian inverse problem for a given system written in the gradient form. I will continue presenting applications of the algorithm to the Lotka-Volterra equation and linear systems. In the case of Lotka-Volterra equations, this algorithm generalizes the well-known use of gauge transformations to skew-symmetrize the interaction matrix of a LV system which leads to a Hamiltonian description of LV systems.