Nonlinear dynamics is a rapidly developing subject across all disciplines involving spatial or temporal evolution. The reconstruction of the equations of motion for a nonlinear system from observed time series has been a hot topic for a long time. Nevertheless, in practice only partial information is available for many systems which are very likely contaminated with noise. Here, based on the invariance of the evolution equation during time translation, a globally valid local approximation of the trajectory is determined, which could be reliably used for the reconstruction of the vector fields with unknown parameters or functional forms, even with partial information of the state evolution. The global consideration very effectively alleviates noise interference and bestows exceptional robustness to the technique, which asks only for solution of linear equations and thus is very efficient. The new scheme is nicely demonstrated in the Lorenz equation in different conditions, while an FHN neural network model is used to show its strength in high-dimensions.