Stochastic averaging and sensitivity analysis for two scale reaction networks

Hashemi, Araz; Núñez, Marcel; Plecháč, Petr; Vlachos, Dionisios G.

doi:10.1063/1.4942008

Title: Stochastic averaging and sensitivity analysis for two scale reaction networks

Abstract

In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate computations for obtaining estimates of expected values and sensitivities with respect to the steady state distribution. A two-time-scale formulation is used to establish bounds on the bias induced by the averaging method. Further, this formulation provides a framework to create an accelerated “averaged” version of most single-scale sensitivity estimation methods. In particular, we propose the use of a centered ergodic likelihood ratio method for steady state estimation and show how one can adapt it to accelerated simulations of multiscale systems. Lastly, we develop an adaptive “batch-means” stopping rule for determining when to terminate the micro-equilibration process.

Authors:

Hashemi, Araz ^[1]; Núñez, Marcel ^[1]; Plecháč, Petr ^[1]; Vlachos, Dionisios G. ^[1]

Univ. of Delaware, Newark, DE (United States)

Publication Date:: Wed Feb 17 00:00:00 EST 2016

Research Org.:: Univ. of Delaware, Newark, DE (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1469682

Alternate Identifier(s):: OSTI ID: 1238296

Grant/Contract Number:: SC0010549

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 144; Journal Issue: 7; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats


                    Hashemi, Araz, Núñez, Marcel, Plecháč, Petr, and Vlachos, Dionisios G. Stochastic averaging and sensitivity analysis for two scale reaction networks.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4942008.

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                    Hashemi, Araz, Núñez, Marcel, Plecháč, Petr, & Vlachos, Dionisios G. Stochastic averaging and sensitivity analysis for two scale reaction networks.  United States.  https://doi.org/10.1063/1.4942008

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                    Hashemi, Araz, Núñez, Marcel, Plecháč, Petr, and Vlachos, Dionisios G. Wed .  
"Stochastic averaging and sensitivity analysis for two scale reaction networks".  United States.  https://doi.org/10.1063/1.4942008.  https://www.osti.gov/servlets/purl/1469682.

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@article{osti_1469682,

  title        = {Stochastic averaging and sensitivity analysis for two scale reaction networks},

  author       = {Hashemi, Araz and Núñez, Marcel and Plecháč, Petr and Vlachos, Dionisios G.},

  abstractNote = {In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate computations for obtaining estimates of expected values and sensitivities with respect to the steady state distribution. A two-time-scale formulation is used to establish bounds on the bias induced by the averaging method. Further, this formulation provides a framework to create an accelerated “averaged” version of most single-scale sensitivity estimation methods. In particular, we propose the use of a centered ergodic likelihood ratio method for steady state estimation and show how one can adapt it to accelerated simulations of multiscale systems. Lastly, we develop an adaptive “batch-means” stopping rule for determining when to terminate the micro-equilibration process.},

  doi          = {10.1063/1.4942008},

  journal      = {Journal of Chemical Physics},

  number       = 7,

  volume       = 144,

  place        = {United States},

  year         = {Wed Feb 17 00:00:00 EST 2016},

  month        = {Wed Feb 17 00:00:00 EST 2016}

}

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Linear Algebra and its Applications, Vol. 76
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An optimal Finite State Projection Method
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Sunkara, Vikram; Hegland, Markus
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Works referencing / citing this record:

Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling
journal, October 2017

Núñez, M.; Robie, T.; Vlachos, D. G.
The Journal of Chemical Physics, Vol. 147, Issue 16
DOI: 10.1063/1.4998926

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Title: Stochastic averaging and sensitivity analysis for two scale reaction networks

Abstract

Citation Formats

Sensitivity of the stationary distribution vector for an ergodic Markov chain journal, April 1986

Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems journal, July 2005

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

Simulation Output Analysis Using Standardized Time Series journal, February 1990

Continuous Time Markov Chain Models for Chemical Reaction Networks book, January 2011

Practical Markov Chain Monte Carlo journal, November 1992

The finite state projection algorithm for the solution of the chemical master equation journal, January 2006

Implementing the batch means method in simulation experiments conference, January 1996

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

Avoiding negative populations in explicit Poisson tau-leaping journal, August 2005

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

An optimal Finite State Projection Method journal, May 2010

Approximate accelerated stochastic simulation of chemically reacting systems journal, July 2001

Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm journal, October 2005

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

Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting journal, March 2012

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

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

Efficient stochastic sensitivity analysis of discrete event systems journal, February 2007

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

Steady state likelihood ratio sensitivity analysis for stiff kinetic Monte Carlo simulations journal, January 2015

Sensitivity analysis for stochastic chemical reaction networks with multiple time-scales journal, January 2014

Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions journal, March 1986

An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains journal, January 2012

Binomial leap methods for simulating stochastic chemical kinetics journal, December 2004

Continuous-Time Markov Chains and Applications: A Two-Time-Scale Approach book, January 2013

Likelihood ratio gradient estimation for stochastic systems journal, October 1990

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

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions journal, February 2005

Parametric sensitivity analysis for biochemical reaction networks based on pathwise information theory journal, January 2013

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods journal, February 2007

Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales journal, January 2007

Markov Processes: Characterization and Convergence book, March 1986

Efficient gradient estimation using finite differencing and likelihood ratios for kinetic Monte Carlo simulations journal, August 2012

Strong Convergence and Speed up of Nested Stochastic Simulation Algorithm journal, April 2014

The slow-scale stochastic simulation algorithm journal, January 2005

An efficient and unbiased method for sensitivity analysis of stochastic reaction networks journal, December 2014

Sensitivity of the stationary distribution vector for an ergodic Markov chain journal, April 1986

An optimal Finite State Projection Method journal, May 2010

Efficiency of the Girsanov Transformation Approach for Parametric Sensitivity Analysis of Stochastic Chemical Kinetics journal, January 2016

Implementing the batch means method in simulation experiments conference, January 1996

An efficient and unbiased method for sensitivity analysis of stochastic reaction networks preprint, January 2014

Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling journal, October 2017

Sensitivity of the stationary distribution vector for an ergodic Markov chain
journal, April 1986

Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems
journal, July 2005

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

Simulation Output Analysis Using Standardized Time Series
journal, February 1990

Continuous Time Markov Chain Models for Chemical Reaction Networks
book, January 2011

Practical Markov Chain Monte Carlo
journal, November 1992

The finite state projection algorithm for the solution of the chemical master equation
journal, January 2006

Implementing the batch means method in simulation experiments
conference, January 1996

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

Avoiding negative populations in explicit Poisson tau-leaping
journal, August 2005

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

An optimal Finite State Projection Method
journal, May 2010

Approximate accelerated stochastic simulation of chemically reacting systems
journal, July 2001

Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm
journal, October 2005

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

Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting
journal, March 2012

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

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

Efficient stochastic sensitivity analysis of discrete event systems
journal, February 2007

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

Steady state likelihood ratio sensitivity analysis for stiff kinetic Monte Carlo simulations
journal, January 2015

Sensitivity analysis for stochastic chemical reaction networks with multiple time-scales
journal, January 2014

Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
journal, March 1986

An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains
journal, January 2012

Binomial leap methods for simulating stochastic chemical kinetics
journal, December 2004

Continuous-Time Markov Chains and Applications: A Two-Time-Scale Approach
book, January 2013

Likelihood ratio gradient estimation for stochastic systems
journal, October 1990

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

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions
journal, February 2005

Parametric sensitivity analysis for biochemical reaction networks based on pathwise information theory
journal, January 2013

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods
journal, February 2007

Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales
journal, January 2007

Markov Processes: Characterization and Convergence
book, March 1986

Efficient gradient estimation using finite differencing and likelihood ratios for kinetic Monte Carlo simulations
journal, August 2012

Strong Convergence and Speed up of Nested Stochastic Simulation Algorithm
journal, April 2014

The slow-scale stochastic simulation algorithm
journal, January 2005

An efficient and unbiased method for sensitivity analysis of stochastic reaction networks
journal, December 2014

Sensitivity of the stationary distribution vector for an ergodic Markov chain
journal, April 1986

An optimal Finite State Projection Method
journal, May 2010

Efficiency of the Girsanov Transformation Approach for Parametric Sensitivity Analysis of Stochastic Chemical Kinetics
journal, January 2016

Implementing the batch means method in simulation experiments
conference, January 1996

An efficient and unbiased method for sensitivity analysis of stochastic reaction networks
preprint, January 2014

Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling
journal, October 2017