Information-Theoretic Approach for Model Reduction Over Finite Time Horizon

TL;DR

This paper introduces an information-theoretic framework for finite time model reduction, proposing a new n-step KL rate metric and information transfer measure to better assess and reduce models over finite horizons.

Contribution

It generalizes KL divergence-based metrics for finite time horizons and integrates them into a new approach for model reduction using information transfer, applicable to linear and potentially nonlinear systems.

Findings

The n-step KL rate metric effectively compares models over finite horizons.

Information transfer quantifies the influence of states for model reduction.

Application demonstrates improved finite time model reduction.

Abstract

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.