Undershooting: modeling dynamical systems by time grid refinements

Building models of dynamical systems on the basis of observed data, the time grid of the data is typically the same as the time grid of the model. We show that a refinement of the model time grid relative to a wider-meshed time grid of the data provides deeper insights into the dynamics. This "undershooting" can be derived from the principle of uniform causality. Combining undershoot- ing with recurrent error correction neural networks (3), lead to a novel approach which improves the performance of our models by time grid refinements.