Inference of reaction rate parameters based on summary statistics from experiments

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin; Sargsyan, Khachik; Najm, Habib N.

doi:10.1016/j.proci.2016.08.058

Title: Inference of reaction rate parameters based on summary statistics from experiments

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Abstract

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H₂/O₂-mechanism chain branching reaction H + O₂ → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inferencemore »« less

Authors:

Khalil, Mohammad ^[1]; Chowdhary, Kamaljit Singh ^[1]; Safta, Cosmin ^[1]; Sargsyan, Khachik ^[1]; Najm, Habib N. ^[1]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Publication Date:: Sat Oct 15 00:00:00 EDT 2016

Research Org.:: Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1325156

Alternate Identifier(s):: OSTI ID: 1397963

Report Number(s):: SAND-2016-4787J
Journal ID: ISSN 1540-7489; 640507

Grant/Contract Number:: AC04-94AL85000; AC04-94-AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Proceedings of the Combustion Institute

Additional Journal Information:: Journal Name: Proceedings of the Combustion Institute; Journal ID: ISSN 1540-7489

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; uncertainty quantification; Bayesian inference; reaction rates; Arrhenius parameters; shock tube experiments

Citation Formats


                    Khalil, Mohammad, Chowdhary, Kamaljit Singh, Safta, Cosmin, Sargsyan, Khachik, and Najm, Habib N. Inference of reaction rate parameters based on summary statistics from experiments.  United States: N. p., 2016. 
Web.  doi:10.1016/j.proci.2016.08.058.

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                    Khalil, Mohammad, Chowdhary, Kamaljit Singh, Safta, Cosmin, Sargsyan, Khachik, & Najm, Habib N. Inference of reaction rate parameters based on summary statistics from experiments.  United States.  https://doi.org/10.1016/j.proci.2016.08.058

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                    Khalil, Mohammad, Chowdhary, Kamaljit Singh, Safta, Cosmin, Sargsyan, Khachik, and Najm, Habib N. Sat .  
"Inference of reaction rate parameters based on summary statistics from experiments".  United States.  https://doi.org/10.1016/j.proci.2016.08.058.  https://www.osti.gov/servlets/purl/1325156.

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@article{osti_1325156,

  title        = {Inference of reaction rate parameters based on summary statistics from experiments},

  author       = {Khalil, Mohammad and Chowdhary, Kamaljit Singh and Safta, Cosmin and Sargsyan, Khachik and Najm, Habib N.},

  abstractNote = {Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H2/O2-mechanism chain branching reaction H + O2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.},

  doi          = {10.1016/j.proci.2016.08.058},

  journal      = {Proceedings of the Combustion Institute},

  number       = ,

  volume       = ,

  place        = {United States},

  year         = {Sat Oct 15 00:00:00 EDT 2016},

  month        = {Sat Oct 15 00:00:00 EDT 2016}

}

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