ADM-CLE approach for detecting slow variables in continuous time Markov chains and dynamic data

TL;DR

The paper introduces ADM-CLE, a novel method combining anisotropic diffusion maps with chemical Langevin equation approximations to efficiently detect slow variables in high-dimensional stochastic chemical reaction networks, enabling better analysis of their stationary distributions.

Contribution

It develops the ADM-CLE approach that improves efficiency over traditional ADM by replacing simulation steps with CLE-based approximations for detecting slow variables.

Findings

ADM-CLE effectively identifies slow variables in complex chemical networks.

The method estimates stationary distributions without prior knowledge.

It reduces computational cost compared to standard ADM.

Abstract

A method for detecting intrinsic slow variables in high-dimensional stochastic chemical reaction networks is developed and analyzed. It combines anisotropic diffusion maps (ADM) with approximations based on the chemical Langevin equation (CLE). The resulting approach, called ADM-CLE, has the potential of being more efficient than the ADM method for a large class of chemical reaction systems, because it replaces the computationally most expensive step of ADM (running local short bursts of simulations) by using an approximation based on the CLE. The ADM-CLE approach can be used to estimate the stationary distribution of the detected slow variable, without any a-priori knowledge of it. If the conditional distribution of the fast variables can be obtained analytically, then the resulting ADM-CLE approach does not make any use of Monte Carlo simulations to estimate the distributions of both slow and fast variables.