In this article, we consider a system of parametric ODEs which involves unknown parameters and we seek to identify the values of the parameters associated to a given measurement. To do so, we place ourselves within the fairly usual framework that this single measurement is in fact taken from a population of data and we therefore want to take advantage of the statistical knowledge about the population to regularize the classical minimization problem associated to our identification problem. In the method that we propose and that we call the Latent Variable Gradient Flow method, the data set is represented by an autoencoder neural network which allows to associate to each element of the data set a latent variable. Then, introducing a non-linear mapping between the parameter space and the latent variable space allows to convexify the cost function and to demonstrate convergence properties. These properties are numerically illustrated with different tests on Van der Pol and FitzHugh-Nagumo models.