Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Navarro Jimenez, M.; Le Maître, O. P.; Knio, O. M.

doi:10.1063/1.4971797

Title: Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Abstract

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. Here, a sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysismore »« less

Authors:

Navarro Jimenez, M. ^[1];

^[2]; Knio, O. M. ^[3]

King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia). CEMSE Division
King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia). CEMSE Division; Univ. Paris-Saclay, Gif-sur-Yvette (France). LIMSI and CNRS
King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia). CEMSE Division; Duke Univ., Durham, NC (United States). Dept. of Mechanical Engineering and Materials Science

Publication Date:: Fri Dec 23 00:00:00 EST 2016

Research Org.:: Duke Univ., Durham, NC (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia)

OSTI Identifier:: 1423885

Alternate Identifier(s):: OSTI ID: 1337433

Grant/Contract Number:: SC0008789

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 145; Journal Issue: 24; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Stochastic Process; Poisson's equation; Decomposition reactions; nonlinear dynamics; monte carlo methods; modeling; probability theory; real functions; mathematical physics; partial differential equations; reaction mechanisms

Citation Formats


                    Navarro Jimenez, M., Le Maître, O. P., and Knio, O. M. Global sensitivity analysis in stochastic simulators of uncertain reaction networks.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4971797.

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                    Navarro Jimenez, M., Le Maître, O. P., & Knio, O. M. Global sensitivity analysis in stochastic simulators of uncertain reaction networks.  United States.  https://doi.org/10.1063/1.4971797

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                    Navarro Jimenez, M., Le Maître, O. P., and Knio, O. M. Fri .  
"Global sensitivity analysis in stochastic simulators of uncertain reaction networks".  United States.  https://doi.org/10.1063/1.4971797.  https://www.osti.gov/servlets/purl/1423885.

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@article{osti_1423885,

  title        = {Global sensitivity analysis in stochastic simulators of uncertain reaction networks},

  author       = {Navarro Jimenez, M. and Le Maître, O. P. and Knio, O. M.},

  abstractNote = {Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. Here, a sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.},

  doi          = {10.1063/1.4971797},

  journal      = {Journal of Chemical Physics},

  number       = 24,

  volume       = 145,

  place        = {United States},

  year         = {Fri Dec 23 00:00:00 EST 2016},

  month        = {Fri Dec 23 00:00:00 EST 2016}

}

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Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
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Works referencing / citing this record:

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates
journal, December 2018

Vohra, Manav; Alexanderian, Alen; Safta, Cosmin
Journal of Scientific Computing, Vol. 79, Issue 2
DOI: 10.1007/s10915-018-0894-4

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Title: Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Abstract

Citation Formats

Polynomial chaos expansion for sensitivity analysis journal, July 2009

Approximation of Population Processes book, January 1981

Analysis of variance designs for model output journal, March 1999

Uncertainty Quantification in MD Simulations. Part I: Forward Propagation journal, January 2012

Automatic identification of model reductions for discrete stochastic simulation journal, July 2012

Preconditioned Bayesian Regression for Stochastic Chemical Kinetics journal, July 2013

Variance decomposition in stochastic simulators journal, June 2015

Binomial distribution based τ-leap accelerated stochastic simulation journal, January 2005

Hybrid Chernoff Tau-Leap journal, January 2014

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks journal, January 2010

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore journal, May 2013

Sensitivity Analysis in Chemical Kinetics journal, October 1983

Reduction of chemical reaction networks through delay distributions journal, March 2013

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels journal, March 2000

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. II. Uncertain potential parameters journal, May 2013

Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics journal, January 2012

A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems journal, January 2012

Spectral stochastic uncertainty quantification in chemical systems journal, September 2004

Error analysis of tau-leap simulation methods journal, December 2011

Constructing stochastic models from deterministic process equations by propensity adjustment journal, January 2011

Stochastic Finite Elements: A Spectral Approach book, January 1991

PC analysis of stochastic differential equations driven by Wiener noise journal, March 2015

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems journal, January 2015

Efficient step size selection for the tau-leaping simulation method journal, January 2006

An adaptive multi-level simulation algorithm for stochastic biological systems journal, January 2015

Exact stochastic simulation of coupled chemical reactions journal, December 1977

Multilevel Monte Carlo Path Simulation journal, June 2008

Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics book, January 2010

Making best use of model evaluations to compute sensitivity indices journal, May 2002

The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions journal, January 2012

Derivative based global sensitivity measures and their link with global sensitivity indices journal, June 2009

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method journal, December 2003

Master Equations, Stochastic Differential Equations, and Bifurcations journal, February 1979

Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index journal, February 2010

The subtle business of model reduction for stochastic chemical kinetics journal, February 2009

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions journal, December 1976

A modified next reaction method for simulating chemical systems with time dependent propensities and delays journal, December 2007

Sensitivity Analysis for Chemical Models journal, July 2005

A finite difference method for estimating second order parameter sensitivities of discrete stochastic chemical reaction networks journal, December 2012

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates journal, December 2018

Polynomial chaos expansion for sensitivity analysis
journal, July 2009

Approximation of Population Processes
book, January 1981

Analysis of variance designs for model output
journal, March 1999

Uncertainty Quantification in MD Simulations. Part I: Forward Propagation
journal, January 2012

Automatic identification of model reductions for discrete stochastic simulation
journal, July 2012

Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
journal, July 2013

Variance decomposition in stochastic simulators
journal, June 2015

Binomial distribution based τ-leap accelerated stochastic simulation
journal, January 2005

Hybrid Chernoff Tau-Leap
journal, January 2014

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks
journal, January 2010

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore
journal, May 2013

Sensitivity Analysis in Chemical Kinetics
journal, October 1983

Reduction of chemical reaction networks through delay distributions
journal, March 2013

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels
journal, March 2000

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. II. Uncertain potential parameters
journal, May 2013

Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics
journal, January 2012

A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems
journal, January 2012

Spectral stochastic uncertainty quantification in chemical systems
journal, September 2004

Error analysis of tau-leap simulation methods
journal, December 2011

Constructing stochastic models from deterministic process equations by propensity adjustment
journal, January 2011

Stochastic Finite Elements: A Spectral Approach
book, January 1991

PC analysis of stochastic differential equations driven by Wiener noise
journal, March 2015

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems
journal, January 2015

Efficient step size selection for the tau-leaping simulation method
journal, January 2006

An adaptive multi-level simulation algorithm for stochastic biological systems
journal, January 2015

Exact stochastic simulation of coupled chemical reactions
journal, December 1977

Multilevel Monte Carlo Path Simulation
journal, June 2008

Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics
book, January 2010

Making best use of model evaluations to compute sensitivity indices
journal, May 2002

The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions
journal, January 2012

Derivative based global sensitivity measures and their link with global sensitivity indices
journal, June 2009

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method
journal, December 2003

Master Equations, Stochastic Differential Equations, and Bifurcations
journal, February 1979

Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index
journal, February 2010

The subtle business of model reduction for stochastic chemical kinetics
journal, February 2009

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
journal, December 1976

A modified next reaction method for simulating chemical systems with time dependent propensities and delays
journal, December 2007

Sensitivity Analysis for Chemical Models
journal, July 2005

A finite difference method for estimating second order parameter sensitivities of discrete stochastic chemical reaction networks
journal, December 2012

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates
journal, December 2018