Academic Journal
A Provably Convergent Control Closure Scheme for the Method of Moments of the Chemical Master Equation
| العنوان: | A Provably Convergent Control Closure Scheme for the Method of Moments of the Chemical Master Equation |
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| المؤلفون: | Vincent Wagner, Robin Strässer, Frank Allgöwer, Nicole Radde |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | Biotechnology, Infectious Diseases, Environmental Sciences not elsewhere classified, Biological Sciences not elsewhere classified, Mathematical Sciences not elsewhere classified, Chemical Sciences not elsewhere classified, Physical Sciences not elsewhere classified, provide probability bounds, nonlinear dynamical system, closed since lower, chemical master equation, priori moment estimates, estimated moment trajectories, model predictive control, proposed method offers, order moments depend, closing moments serve, order moments, moments serve, moment equations, control input, statistical moments, time evolution, stochastic simulations, ranging implications, polynomial systems, n <, many fields, including biology, convergence properties |
| الوصف: | 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 calculate the first n m 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 n m moments serve as states, and the closing moments serve as the control input. We demonstrate the efficacy of our approach using three 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 the 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. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | unknown |
| Relation: | https://figshare.com/articles/journal_contribution/A_Provably_Convergent_Control_Closure_Scheme_for_the_Method_of_Moments_of_the_Chemical_Master_Equation/24747722 |
| DOI: | 10.1021/acs.jctc.3c00548.s001 |
| الاتاحة: | https://doi.org/10.1021/acs.jctc.3c00548.s001 https://figshare.com/articles/journal_contribution/A_Provably_Convergent_Control_Closure_Scheme_for_the_Method_of_Moments_of_the_Chemical_Master_Equation/24747722 |
| Rights: | CC BY-NC 4.0 |
| رقم الانضمام: | edsbas.D0AF3E1E |
| قاعدة البيانات: | BASE |
| DOI: | 10.1021/acs.jctc.3c00548.s001 |
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