  Solution of Ordinary Differential Equation (ODE) model of dynamical system
may not agree with its observed values. Often this discrepancy can be
attributed to unmodeled forcings in the evolution rule of the dynamical system.
In this article, an approach for data-based model improvement is described
which exploits the geometric constraints imposed by the system observations to
estimate these unmodeled terms. The nominal model is augmented using these
extra forcing terms to make predictions. This approach is applied to
navigational satellite orbit prediction to bring down the error to
approximately 12% of the error when using the nominal force model for a 2-hour
prediction. In another example improved temperature predictions over the
nominal heat equation are obtained for one-dimensional conduction.
