In this article, we introduce a novel moment closure scheme based on concepts from Model Predictive Control (MPC) to accurately describe the time evolution of the statistical moments of the solution of the Chemical Master Equation (CME). The Method of Moments, a set of ordinary differential equations frequently used to consider the first nm moments, is generally not closed since lower-order moments depend on higher-order moments. To overcome this limitation, we interpret the moment equations as a nonlinear dynamical system, where the first nm moments serve as states and the closing moments serve as control input. We demonstrate the efficacy of our approach using two example systems and show that it outperforms existing closure schemes. For polynomial systems, which encompass all mass-action systems, we provide probability bounds for the error between true and estimated moment trajectories. We achieve this by combining convergence properties of a priori moment estimates from stochastic simulations with guarantees for nonlinear reference tracking MPC. Our proposed method offers an effective solution to accurately predict the time evolution of moments of the CME, which has wide-ranging implications for many fields, including biology, chemistry, and engineering.Competing Interest StatementThe authors have declared no competing interest.
%0 Journal Article
%1 Wagner23b
%A Wagner, Vincent
%A Strässer, Robin
%A Allgöwer, Frank
%A Radde, Nicole Erika
%D 2023
%I ACS Publications
%J Journal of Chemical Theory and Computation
%K exc2075 myown pn2
%N 24
%P 9049–9059
%R https://doi.org/10.1021/acs.jctc.3c00548
%T A provably convergent control closure scheme for the Method of Moments of the Chemical Master Equation
%U https://pubs.acs.org/doi/full/10.1021/acs.jctc.3c00548
%V 19
%X In this article, we introduce a novel moment closure scheme based on concepts from Model Predictive Control (MPC) to accurately describe the time evolution of the statistical moments of the solution of the Chemical Master Equation (CME). The Method of Moments, a set of ordinary differential equations frequently used to consider the first nm moments, is generally not closed since lower-order moments depend on higher-order moments. To overcome this limitation, we interpret the moment equations as a nonlinear dynamical system, where the first nm moments serve as states and the closing moments serve as control input. We demonstrate the efficacy of our approach using two example systems and show that it outperforms existing closure schemes. For polynomial systems, which encompass all mass-action systems, we provide probability bounds for the error between true and estimated moment trajectories. We achieve this by combining convergence properties of a priori moment estimates from stochastic simulations with guarantees for nonlinear reference tracking MPC. Our proposed method offers an effective solution to accurately predict the time evolution of moments of the CME, which has wide-ranging implications for many fields, including biology, chemistry, and engineering.Competing Interest StatementThe authors have declared no competing interest.
@article{Wagner23b,
abstract = {In this article, we introduce a novel moment closure scheme based on concepts from Model Predictive Control (MPC) to accurately describe the time evolution of the statistical moments of the solution of the Chemical Master Equation (CME). The Method of Moments, a set of ordinary differential equations frequently used to consider the first nm moments, is generally not closed since lower-order moments depend on higher-order moments. To overcome this limitation, we interpret the moment equations as a nonlinear dynamical system, where the first nm moments serve as states and the closing moments serve as control input. We demonstrate the efficacy of our approach using two example systems and show that it outperforms existing closure schemes. For polynomial systems, which encompass all mass-action systems, we provide probability bounds for the error between true and estimated moment trajectories. We achieve this by combining convergence properties of a priori moment estimates from stochastic simulations with guarantees for nonlinear reference tracking MPC. Our proposed method offers an effective solution to accurately predict the time evolution of moments of the CME, which has wide-ranging implications for many fields, including biology, chemistry, and engineering.Competing Interest StatementThe authors have declared no competing interest.},
added-at = {2023-05-04T08:38:19.000+0200},
author = {Wagner, Vincent and Str{\"a}sser, Robin and Allg{\"o}wer, Frank and Radde, Nicole Erika},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/22b0d6952a32448eb9fa75cc34c4501bd/vincentwagner},
doi = {https://doi.org/10.1021/acs.jctc.3c00548},
elocation-id = {2023.05.03.539185},
eprint = {https://www.biorxiv.org/content/early/2023/05/03/2023.05.03.539185.full.pdf},
interhash = {b962c410c4ef09d96fa6fc22ed1e81f9},
intrahash = {2b0d6952a32448eb9fa75cc34c4501bd},
journal = {Journal of Chemical Theory and Computation},
keywords = {exc2075 myown pn2},
month = {12},
number = 24,
pages = {9049–9059},
preprinturl = {https://www.biorxiv.org/content/10.1101/2023.05.03.539185v2},
publisher = {ACS Publications},
timestamp = {2024-01-10T08:47:36.000+0100},
title = {A provably convergent control closure scheme for the Method of Moments of the Chemical Master Equation},
url = {https://pubs.acs.org/doi/full/10.1021/acs.jctc.3c00548},
volume = 19,
year = 2023
}
