A numerical procedure for model reduction using the generalized Langevin equation formalism

TL;DR

This paper introduces a numerical method to reconstruct generalized Langevin equations from data, enabling model reduction and nonlinear time series analysis, with successful tests on biological networks.

Contribution

It develops a novel numerical procedure to reconstruct GLEs from data, extending their application to systems not obeying detailed balance.

Findings

High accuracy in reproducing full model dynamics

Effective application to biological networks

Potential for nonlinear time series analysis

Abstract

The Zwanzig-Mori pro jection formalism is widely used in studying systems with many degrees of freedom. Recently Xing and Kim used the pro jection formalism and derived the generalized Langevin equations (GLEs) for a general stochastic system not necessarily obeying detailed balance. In this study we develop a numerical procedure to reconstruct the GLEs from data. Numerical tests on two biological networks show remarkable agreement between the results calculated from the reconstructed GLEs and those of full model simulations. We suggest that the procedure can be applied in model reduction and a novel way of nonlinear time series analysis.