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Implementation of variable parameters in the Krylov-based finite state projection for solving the chemical master equation. (English) Zbl 1411.65070
Summary: The finite state projection (FSP) algorithm is a reduction method for solving the chemical master equation (CME). The Krylov-FSP improved on the original FSP by using an embedded scheme where the action of the matrix exponential is evaluated by the Krylov subspace method of Expokit for greater efficiency. There are parameters that impact the method, such as the stepsize that must be controlled to ensure the accuracy of the computed matrix exponentials, or to ensure the accuracy of the FSP. Other parameters include the dimension of the Krylov basis, or even the extent of reachability when expanding the FSP. In this work, we incorporate adaptive strategies to automatically vary these parameters. Numerical experiments comparing the resulting variants are reported, showing how certain choices perform better than others.

MSC:
65F60 Numerical computation of matrix exponential and similar matrix functions
65L05 Numerical methods for initial value problems
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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[1] Burrage, K.; Hegland, M.; MacNamara, S.; Sidje, R. B., A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems, (Langville, A. N.; Stewart, W. J., Proceedings of the One Hundred and Fiftieth Markov Anniversary Meeting, (2006), Boson Books Charleston, SC, USA), 21-38
[2] Cao, Y.; Gillespie, D. T.; Petzold, L. R., Efficient step size selection for the tau-leaping simulation method., J. Chem. Phys., 124, 4, 044109, (2006)
[3] Gillespie, D. T., Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81, 25, 2340-2361, (1977)
[4] Gillespie, D. T.; Petzold, L. R., Improved leap-size selection for accelerated stochastic simulation, J. Chem. Phys., 119, 16, 8229, (2003)
[5] Goutsias, J., Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems., J. Chem. Phys., 122, 18, 184102, (2005)
[6] MacNamara, S.; Bersani, A. M.; Burrage, K.; Sidje, R. B., Stochastic chemical kinetics and the total quasi-steady-state assumption: application to the stochastic simulation algorithm and chemical master equation, J. Chem. Phys., 129, 9, (2008)
[7] Macnamara, S.; Burrage, K.; Sidje, R. B., Multiscale modeling of chemical kinetics via master equation, Multiscale Model. Simul., 6, 4, 1146-1168, (2008) · Zbl 1153.60370
[8] Mooasvi, A.; Tranquilli, P.; Sandu, A., Solving stochastic chemical kinetics by metropolis-Hastings sampling, J. Appl. Anal. Comput., 6, 2, 322-335, (2016)
[9] Munsky, B.; Khammash, M., The finite state projection algorithm for the solution of the chemical master equation., J. Chem. Phys., 124, 4, 044104, (2006)
[10] Munsky, B.; Khammash, M., A multiple time interval finite state projection algorithm for the solution to the chemical master equation, J. Comput. Phys., 226, 1, 818-835, (2007) · Zbl 1131.82020
[11] Niesen, J.; Wright, W. M., Algorithm 919: a Krylov subspace algorithm for evaluating the ϕ-functions appearing in exponential integrators, ACM Trans. Math. Softw., 38, 3, 22:1-22:19, (2012) · Zbl 1365.65185
[12] Sidje, R. B., Expokit: a software package for computing matrix exponentials, ACM Trans. Math. Softw., 24, 1, 130-156, (1998) · Zbl 0917.65063
[13] Sidje, R. B.; Stewart, W. J., A numerical study of large sparse matrix exponentials arising in Markov chains, Comput. Stat. Data Anal., 29, 3, 345-368, (1999) · Zbl 1042.65508
[14] Tian, T.; Burrage, K., Binomial leap methods for simulating stochastic chemical kinetics., J. Chem. Phys., 121, 21, 10356-10364, (2004)
[15] Wolf, V.; Goel, R.; Mateescu, M.; Henzinger, T. A., Solving the chemical master equation using sliding windows, BMC Syst. Biol., 4, 1, 1-19, (2010)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.