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Preconditioned Bayesian Regression for Stochastic Chemical Kinetics

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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.

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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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Authors and Affiliations

  1. Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78712, USA

    Alen Alexanderian

  2. Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, 27708, USA

    Francesco Rizzi & Omar M. Knio

  3. Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, 21250, USA

    Muruhan Rathinam

  4. LIMSI-CNRS, BP 133, Bt 508, 91403 , Orsay Cedex, France

    Olivier P. Le Maître

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  1. Alen Alexanderian
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  2. Francesco Rizzi
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  4. Olivier P. Le Maître
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  5. Omar M. Knio
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Correspondence to Omar M. Knio.

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Alexanderian, A., Rizzi, F., Rathinam, M. et al. Preconditioned Bayesian Regression for Stochastic Chemical Kinetics. J Sci Comput 58, 592–626 (2014). https://doi.org/10.1007/s10915-013-9745-5

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  • DOI: https://doi.org/10.1007/s10915-013-9745-5

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