  This paper presents an information-theoretic approach for model reduction for
finite time simulation. Although system models are typically used for
simulation over a finite time, most of the metrics (and pseudo-metrics) used
for model accuracy assessment consider asymptotic behavior e.g., Hankel
singular values and Kullback-Leibler(KL) rate metric. These metrics could
further be used for model order reduction. Hence, in this paper, we propose a
generalization of KL divergence-based metric called n-step KL rate metric,
which could be used to compare models over a finite time horizon. We then
demonstrate that the asymptotic metrics for comparing dynamical systems may not
accurately assess the model prediction uncertainties over a finite time
horizon. Motivated by this finite time analysis, we propose a new pragmatic
approach to compute the influence of a subset of states on a combination of
states called information transfer (IT). Model reduction typically involves the
removal or truncation of states. IT combines the concepts from the n-step KL
rate metric and model reduction. Finally, we demonstrate the application of
information transfer for model reduction. Although the analysis and definitions
presented in this paper assume linear systems, they can be extended for
nonlinear systems.
