Preconditioned Bayesian regression for stochastic chemical kinetics

Alen Alexanderian; Francesco Rizzi; Muruhan Rathinam; Olivier P. Le Maître; Omar M. Knio

doi:10.1007/s10915-013-9745-5

Preconditioned Bayesian regression for stochastic chemical kinetics

Alen Alexanderian, Francesco Rizzi, Muruhan Rathinam, Olivier P. Le Maître, Omar M. Knio^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We develop a preconditioned Bayesian regression method that enables sparse polynomial chaos representations of noisy outputs for stochastic chemical systems with uncertain reaction rates. The approach is based on the definition of an appropriate multiscale transformation of the state variables coupled with a Bayesian regression formalism. This enables efficient and robust recovery of both the transient dynamics and the corresponding noise levels. Implementation of the present approach is illustrated through applications to a stochastic Michaelis-Menten dynamics and a higher dimensional example involving a genetic positive feedback loop. In all cases, a stochastic simulation algorithm (SSA) is used to compute the system dynamics. Numerical experiments show that Bayesian preconditioning algorithms can simultaneously accommodate large noise levels and large variability with uncertain parameters, and that robust estimates can be obtained with a small number of SSA realizations.

Original language	English (US)
Pages (from-to)	592-626
Number of pages	35
Journal	Journal of Scientific Computing
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s10915-013-9745-5
State	Published - Mar 2014

Bibliographical note

Funding Information:
Acknowledgments This work was supported by the US Department of Energy (DOE) under Award Numbers DE-SC0001980 and DE-SC0008789. The work of OLM is partially supported by the French Agence Nationale pour la Recherche (Project ANR-2010-Blan-0904) and the GNR MoMaS funded by Andra, Brgm, Cea, Edf, and Irsn. Finally, would like to thank the reviewer for helpful comments on improving this manuscript.

Keywords

Bayesian regression
Chemical kinetics
Polynomial chaos
Preconditioner
Stochastic simulation algorithm

ASJC Scopus subject areas

Software
General Engineering
Computational Mathematics
Theoretical Computer Science
Applied Mathematics
Numerical Analysis
Computational Theory and Mathematics

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10.1007/s10915-013-9745-5

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title = "Preconditioned Bayesian regression for stochastic chemical kinetics",

abstract = "We develop a preconditioned Bayesian regression method that enables sparse polynomial chaos representations of noisy outputs for stochastic chemical systems with uncertain reaction rates. The approach is based on the definition of an appropriate multiscale transformation of the state variables coupled with a Bayesian regression formalism. This enables efficient and robust recovery of both the transient dynamics and the corresponding noise levels. Implementation of the present approach is illustrated through applications to a stochastic Michaelis-Menten dynamics and a higher dimensional example involving a genetic positive feedback loop. In all cases, a stochastic simulation algorithm (SSA) is used to compute the system dynamics. Numerical experiments show that Bayesian preconditioning algorithms can simultaneously accommodate large noise levels and large variability with uncertain parameters, and that robust estimates can be obtained with a small number of SSA realizations.",

keywords = "Bayesian regression, Chemical kinetics, Polynomial chaos, Preconditioner, Stochastic simulation algorithm",

author = "Alen Alexanderian and Francesco Rizzi and Muruhan Rathinam and {Le Ma{\^i}tre}, {Olivier P.} and Knio, {Omar M.}",

note = "Funding Information: Acknowledgments This work was supported by the US Department of Energy (DOE) under Award Numbers DE-SC0001980 and DE-SC0008789. The work of OLM is partially supported by the French Agence Nationale pour la Recherche (Project ANR-2010-Blan-0904) and the GNR MoMaS funded by Andra, Brgm, Cea, Edf, and Irsn. Finally, would like to thank the reviewer for helpful comments on improving this manuscript.",

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doi = "10.1007/s10915-013-9745-5",

language = "English (US)",

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AU - Alexanderian, Alen

AU - Rizzi, Francesco

AU - Rathinam, Muruhan

AU - Le Maître, Olivier P.

AU - Knio, Omar M.

N1 - Funding Information: Acknowledgments This work was supported by the US Department of Energy (DOE) under Award Numbers DE-SC0001980 and DE-SC0008789. The work of OLM is partially supported by the French Agence Nationale pour la Recherche (Project ANR-2010-Blan-0904) and the GNR MoMaS funded by Andra, Brgm, Cea, Edf, and Irsn. Finally, would like to thank the reviewer for helpful comments on improving this manuscript.

PY - 2014/3

Y1 - 2014/3

N2 - We develop a preconditioned Bayesian regression method that enables sparse polynomial chaos representations of noisy outputs for stochastic chemical systems with uncertain reaction rates. The approach is based on the definition of an appropriate multiscale transformation of the state variables coupled with a Bayesian regression formalism. This enables efficient and robust recovery of both the transient dynamics and the corresponding noise levels. Implementation of the present approach is illustrated through applications to a stochastic Michaelis-Menten dynamics and a higher dimensional example involving a genetic positive feedback loop. In all cases, a stochastic simulation algorithm (SSA) is used to compute the system dynamics. Numerical experiments show that Bayesian preconditioning algorithms can simultaneously accommodate large noise levels and large variability with uncertain parameters, and that robust estimates can be obtained with a small number of SSA realizations.

AB - We develop a preconditioned Bayesian regression method that enables sparse polynomial chaos representations of noisy outputs for stochastic chemical systems with uncertain reaction rates. The approach is based on the definition of an appropriate multiscale transformation of the state variables coupled with a Bayesian regression formalism. This enables efficient and robust recovery of both the transient dynamics and the corresponding noise levels. Implementation of the present approach is illustrated through applications to a stochastic Michaelis-Menten dynamics and a higher dimensional example involving a genetic positive feedback loop. In all cases, a stochastic simulation algorithm (SSA) is used to compute the system dynamics. Numerical experiments show that Bayesian preconditioning algorithms can simultaneously accommodate large noise levels and large variability with uncertain parameters, and that robust estimates can be obtained with a small number of SSA realizations.

KW - Bayesian regression

KW - Chemical kinetics

KW - Polynomial chaos

KW - Preconditioner

KW - Stochastic simulation algorithm

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EP - 626

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

ER -

Preconditioned Bayesian regression for stochastic chemical kinetics

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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