Data-Free Inference of Uncertain Parameters in Chemical Models

Najm, Habib N.; Berry, Robert Dan; Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert

doi:10.1615/int.j.uncertaintyquantification.2013005679

Cited by 19 publications

(20 citation statements)

References 48 publications

(62 reference statements)

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“…11 Scatter plot of 50 chains, with the first 1500 burn-in states removed from each chain. Only every 25th chain state is plotted for convenience [17] both ln A and ln E. As already indicated, the ı-factor in the outer chain likelihood controls the tightness of the bounds consistency check and therefore the scatter in the quantiles observed in the figure. Further, the consistency of the data samples from the 50 chains, relative to the actual data behind the statistics, is illustrated in Fig.…”

Section: Chemical Systemmentioning

confidence: 92%

“…The above DFI construction has been employed in a range of problems [3,8,24]. Before moving forward to a discussion of illustrative applications, we give in the following some general remarks regarding the algorithm.…”

Section: Remarksmentioning

confidence: 99%

“…The data D is a collection of 11 pairs of ignition time and initial temperature [24]. The synthetic data from the detailed model before and after corruption by multiplicative i.i.d.…”

Section: Chemical Systemmentioning

confidence: 99%

“…7. With this data, and employing a corresponding data model, we use Bayesian inference [24] to arrive at the posterior density on the two parameters of interest p.ln A; ln EjD/, shown in Fig. 8.…”

Section: Chemical Systemmentioning

confidence: 99%

“…10 A plot of the means, as well as the 5 % and 95 % quantiles from the parameter posteriors from each data chain step, for all 50 chains, and for the last 500 steps from each chain. The left frame shows those for ln A, while the right frame shows those for ln E. The solid lines indicate the corresponding values from the reference posterior [17] I I I Fig. 11 Scatter plot of 50 chains, with the first 1500 burn-in states removed from each chain.…”

Section: Chemical Systemmentioning

confidence: 99%

See 4 more Smart Citations

Inference Given Summary Statistics

Najm¹,

Chowdhary²

2015

Handbook of Uncertainty Quantification

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Section: Chemical Systemmentioning

confidence: 92%

Section: Remarksmentioning

confidence: 99%

“…The data D is a collection of 11 pairs of ignition time and initial temperature [24]. The synthetic data from the detailed model before and after corruption by multiplicative i.i.d.…”

Section: Chemical Systemmentioning

confidence: 99%

Section: Chemical Systemmentioning

confidence: 99%

Section: Chemical Systemmentioning

confidence: 99%

See 3 more Smart Citations

Inference Given Summary Statistics

Najm¹,

Chowdhary²

2015

Handbook of Uncertainty Quantification

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CheKiPEUQ Intro 2: Harnessing Uncertainties from Data Sets, Bayesian Design of Experiments in Chemical Kinetics**

2020

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When choosing experimental conditions, Bayesian statistical tools can predict the experimental choices which will yield the highest information gain. Experimental choices could be temperature, pressure, reaction time, number of measurements, reactor volume, etc.. Three example analyses are presented here, each using the software Chemical Kinetics Parameter Estimation and Uncertainty Quantification (CheKiPEUQ). Information gain is a measure of reduction of uncertainty in a model's parameters. The three chemical system examples presented each illustrate Bayesian Design of Experiments using information gain. In the first chemical example, temperature selection impacts the information gain for the free energy of reaction in a two‐component equilibrium reaction. In the second example, temperature and pressure are explored for a competitive adsorption Langmuir replacement reaction system. The third example is a catalytic membrane reactor which is a culmination of the previous examples. The catalytic membrane reactor has a complex and nonlinear response in the observables which is solved by numerical evaluation. In the three examples, the experimental conditions are treated as design variables for maximizing information gain.

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On the Statistical Calibration of Physical Models

Sargsyan

Najm

Ghanem

2015

Int J of Chemical Kinetics

107

137

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We introduce a novel statistical calibration framework for physical models, relying on probabilistic embedding of model discrepancy error within the model. For clarity of illustration, we take the measurement errors out of consideration, calibrating a chemical model of interest with respect to a more detailed model, considered as "truth" for the present purpose. We employ Bayesian statistical methods for such model-to-model calibration and demonstrate their capabilities on simple synthetic models, leading to a well-defined parameter estimation problem that employs approximate Bayesian computation. The method is then demonstrated on two case studies for calibration of kinetic rate parameters for methane air chemistry, where ignition time information from a detailed elementary-step kinetic model is used to estimate rate coefficients of a simple chemical mechanism. We show that the calibrated model predictions fit the data and that uncertainty in these predictions is consistent in a mean-square sense with the discrepancy from the detailed model data.

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Data-Free Inference of Uncertain Parameters in Chemical Models

Cited by 19 publications

References 48 publications

Inference Given Summary Statistics

Inference Given Summary Statistics

CheKiPEUQ Intro 2: Harnessing Uncertainties from Data Sets, Bayesian Design of Experiments in Chemical Kinetics**

On the Statistical Calibration of Physical Models

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