Livermore, California, United States
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  • Sandia National Laboratories

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    - Present 5 years 2 months

Publications

  • Dimensionality Reduction for Complex Models via Bayesian Compressive Sensing

    International Journal for Uncertainty Quantification

    Uncertainty quantification in complex physical models is often challenged by the computational expense of these models. One often needs to operate under the assumption of sparsely available model simulations. This issue is even more critical when models include a large number of input parameters. This “curse of dimensionality,” in particular, leads to a prohibitively large number of basis terms in spectral methods for uncertainty quantification, such as polynomial chaos (PC) methods. In this…

    Uncertainty quantification in complex physical models is often challenged by the computational expense of these models. One often needs to operate under the assumption of sparsely available model simulations. This issue is even more critical when models include a large number of input parameters. This “curse of dimensionality,” in particular, leads to a prohibitively large number of basis terms in spectral methods for uncertainty quantification, such as polynomial chaos (PC) methods. In this work, we implement a PC-based surrogate model construction that “learns” and retains only the most relevant basis terms of the PC expansion, using sparse Bayesian learning. This dramatically reduces the dimensionality of the problem, making it more amenable to further analysis such as sensitivity or calibration studies. The model of interest is the community land model with about 80 input parameters, which also exhibits non-smooth input-output behavior.We enhanced the methodology by a clustering and classifying procedure that leads to a piecewise-PC surrogate thereby dealing with nonlinearity. We then obtain global sensitivity information for five outputs with respect to all input parameters using less than 10,000 model simulations—a very small number for an 80-dimensional input parameter space.

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  • Uncertainty quantification of reaction mechanisms accounting for correlations introduced by rate rules and fitted Arrhenius parameters

    Combustion and Flame

    We study correlations among uncertain Arrhenius rate parameters in a chemical model for hydrocarbon fuel–air combustion. We consider correlations induced by the use of rate rules for modeling reaction rate constants, as well as those resulting from fitting rate expressions to empirical measurements arriving at a joint probability density for all Arrhenius parameters. We focus on homogeneous ignition in a fuel–air mixture at constant-pressure. We outline a general methodology for this analysis…

    We study correlations among uncertain Arrhenius rate parameters in a chemical model for hydrocarbon fuel–air combustion. We consider correlations induced by the use of rate rules for modeling reaction rate constants, as well as those resulting from fitting rate expressions to empirical measurements arriving at a joint probability density for all Arrhenius parameters. We focus on homogeneous ignition in a fuel–air mixture at constant-pressure. We outline a general methodology for this analysis using polynomial chaos and Bayesian inference methods. We examine the uncertainties in both the Arrhenius parameters and in predicted ignition time, outlining the role of correlations, and considering both accuracy and computational efficiency.

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  • Multiparameter Spectral Representation of Noise-induced Competence in Bacillus Subtilis

    IEEE/ACM Transactions on Computational Biology and Bioinformatics

    In this work, the problem of representing a stochastic forward model output with respect to a large number of input parameters is considered. The methodology is applied to a stochastic reaction network of competence dynamics in Bacillus subtilis bacterium. In particular, the dependence of the competence state on rate constants of underlying reactions is investigated. We base our methodology on Polynomial Chaos (PC) spectral expansions that allow effective propagation of input parameter…

    In this work, the problem of representing a stochastic forward model output with respect to a large number of input parameters is considered. The methodology is applied to a stochastic reaction network of competence dynamics in Bacillus subtilis bacterium. In particular, the dependence of the competence state on rate constants of underlying reactions is investigated. We base our methodology on Polynomial Chaos (PC) spectral expansions that allow effective propagation of input parameter uncertainties to outputs of interest. Given a number of forward model training runs at sampled input parameter values, the PC modes are estimated using a Bayesian framework. As an outcome, these PC modes are described with posterior probability distributions. The resulting expansion can be regarded as an uncertain response function and can further be used as a computationally inexpensive surrogate instead of the original reaction model for subsequent analyses such as calibration or optimization studies. Furthermore, the methodology is enhanced with a classification-based mixture PC formulation that overcomes the difficulties associated with representing potentially nonsmooth input-output relationships. Finally, the global sensitivity analysis based on the multiparameter spectral representation of an observable of interest provides biological insight and reveals the most important reactions and their couplings for the competence dynamics.

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  • Uncertainty Quantification given Discontinuous Model Response and a Limited Number of Model Runs

    SIAM Journal on Scientific Computing

    We outline a methodology for forward uncertainty quantification in systems with uncertain parameters, discontinuous model response, and a limited number of model runs. Our approach involves two stages. First we detect the discontinuity with Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve for arbitrarily distributed input parameters. Then, employing the Rosenblatt transform, we construct spectral representations of the uncertain model output, using…

    We outline a methodology for forward uncertainty quantification in systems with uncertain parameters, discontinuous model response, and a limited number of model runs. Our approach involves two stages. First we detect the discontinuity with Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve for arbitrarily distributed input parameters. Then, employing the Rosenblatt transform, we construct spectral representations of the uncertain model output, using polynomial chaos (PC) expansions on either side of the discontinuity curve, leading to an averaged PC representation of the forward model response that allows efficient uncertainty quantification. We obtain PC modes by either orthogonal projection or Bayesian inference, and argue for a hybrid approach that targets a balance between the accuracy provided by the orthogonal projection and the flexibility provided by the Bayesian inference. The uncertain model output is then computed by taking an ensemble average over PC expansions corresponding to sampled realizations of the discontinuity curve. The methodology is demonstrated on synthetic examples of discontinuous model response with adjustable sharpness and structure.

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  • Sources of cell-to-cell variability in canonical NF-kB signaling pathway inferred from single cell dynamic images

    J. Biol. Chem

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