We propose a local search approach for learning dynamic systems from time-series data, using networks of differential equations as the underlying model. We evaluate the performance of our approach for two scenarios: first, by comparing with an l1-regularization approach under the assumption of a uniformly weighted network for identifying systems of masses and springs; and then on the task of learning gene regulatory networks, where we compare it with the best performers in the DREAM4 challenge using the original dataset for that challenge. Our method consistently improves on the performance of the other methods considered in both scenarios.