Robustly simulating biochemical reaction kinetics using multi-level Monte Carlo approaches

TL;DR

This paper enhances multi-level Monte Carlo methods for simulating biochemical reaction networks by improving variance reduction techniques and ensemble selection to increase robustness, reliability, and computational efficiency.

Contribution

The work introduces an improved variance reduction method and a new ensemble selection mechanism for multi-level Monte Carlo simulations of biochemical networks.

Findings

Enhanced variance reduction improves simulation stability.

New ensemble selection mechanism increases computational efficiency.

Method demonstrates robustness across various biochemical models.

Abstract

In this work, we consider the problem of estimating summary statistics to characterise biochemical reaction networks of interest. Such networks are often described using the framework of the Chemical Master Equation (CME). For physically-realistic models, the CME is widely considered to be analytically intractable. A variety of Monte Carlo algorithms have therefore been developed to explore the dynamics of such networks empirically. Amongst them is the multi-level method, which uses estimates from multiple ensembles of sample paths of different accuracies to estimate a summary statistic of interest. {In this work, we develop the multi-level method in two directions: (1) to increase the robustness, reliability and performance of the multi-level method, we implement an improved variance reduction method for generating the sample paths of each ensemble; and (2) to improve computational performance, we demonstrate the successful use of a different mechanism for choosing which ensembles should be included in the multi-level algorithm.