Publications

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The move towards extreme-scale computing platforms challenges scientific simula- tions in many ways. Given the recent tendencies in computer architecture development, one needs to reformulate legacy codes in order to cope with large amounts of commu- nication, system faults and requirements of low-memory usage per core. In this work, we develop a novel framework for solving partial differential equa- tions (PDEs) via domain decomposition that reformulates the solution as a state-of- knowledge with a probabilistic interpretation. Such reformulation allows resiliency with respect to potential faults without having to apply fault detection, avoids unnecessary communication and is generally well-positioned for rigorous uncertainty quantification studies that target improvements of predictive fidelity of scientific models. We demon- strate our algorithm for one-dimensional PDE examples where artificial faults have been implemented as bit-flips in the binary representation of subdomain solutions. *Sandia National Laboratories, 7011 East Ave, MS 9051, Livermore, CA 94550 (ksargsy@sandia.gov). t Sandia National Laboratories, Livermore, CA (fnrizzi@sandia.gov). IDuke University, Durham, NC (paul .mycek@duke . edu). Sandia National Laboratories, Livermore, CA (csaft a@sandia.gov). i llSandia National Laboratories, Livermore, CA (knmorri@sandia.gov). II Sandia National Laboratories, Livermore, CA (hnnajm@sandia.gov). **Laboratoire d'Informatique pour la Mecanique et les Sciences de l'Ingenieur, Orsay, France (olm@limsi . f r). ttDuke University, Durham, NC (omar . knio@duke . edu). It Sandia National Laboratories, Livermore, CA (bjdebus@sandia.gov).

In this paper we present a basis selection method that can be used with ℓ1-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets that have more terms in important dimensions and limits the number of unimportant terms that increase mutual coherence and thus degrade the performance of ℓ1-minimization. The important features and the accuracy of basis selection are demonstrated with a number of numerical examples. Specifically, we show that for a given computational budget, basis selection produces a more accurate PCE than would be obtained if the basis were fixed a priori. We also demonstrate that basis selection can be applied with non-uniform random variables and can leverage gradient information.

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Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.

In this paper, a series of algorithms are proposed to address the problems in the NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge. A Bayesian approach is employed to characterize and calibrate the epistemic parameters based on the available data, whereas a variance-based global sensitivity analysis is used to rank the epistemic and aleatory model parameters. A nested sampling of the aleatory-epistemic space is proposed to propagate uncertainties from model parameters to output quantities of interest.

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This brief report explains the method used for parameter calibration and model validation in SST/Macro and the set of tools and workflow developed for this purpose.

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In this project we have developed atmospheric measurement capabilities and a suite of atmospheric modeling and analysis tools that are well suited for verifying emissions of green- house gases (GHGs) on an urban-through-regional scale. We have for the first time applied the Community Multiscale Air Quality (CMAQ) model to simulate atmospheric CO₂ . This will allow for the examination of regional-scale transport and distribution of CO₂ along with air pollutants traditionally studied using CMAQ at relatively high spatial and temporal resolution with the goal of leveraging emissions verification efforts for both air quality and climate. We have developed a bias-enhanced Bayesian inference approach that can remedy the well-known problem of transport model errors in atmospheric CO₂ inversions. We have tested the approach using data and model outputs from the TransCom3 global CO₂ inversion comparison project. We have also performed two prototyping studies on inversion approaches in the generalized convection-diffusion context. One of these studies employed Polynomial Chaos Expansion to accelerate the evaluation of a regional transport model and enable efficient Markov Chain Monte Carlo sampling of the posterior for Bayesian inference. The other approach uses de- terministic inversion of a convection-diffusion-reaction system in the presence of uncertainty. These approaches should, in principle, be applicable to realistic atmospheric problems with moderate adaptation. We outline a regional greenhouse gas source inference system that integrates (1) two ap- proaches of atmospheric dispersion simulation and (2) a class of Bayesian inference and un- certainty quantification algorithms. We use two different and complementary approaches to simulate atmospheric dispersion. Specifically, we use a Eulerian chemical transport model CMAQ and a Lagrangian Particle Dispersion Model - FLEXPART-WRF. These two models share the same WRF assimilated meteorology fields, making it possible to perform a hybrid simulation, in which the Eulerian model (CMAQ) can be used to compute the initial condi- tion needed by the Lagrangian model, while the source-receptor relationships for a large state vector can be efficiently computed using the Lagrangian model in its backward mode. In ad- dition, CMAQ has a complete treatment of atmospheric chemistry of a suite of traditional air pollutants, many of which could help attribute GHGs from different sources. The inference of emissions sources using atmospheric observations is cast as a Bayesian model calibration problem, which is solved using a variety of Bayesian techniques, such as the bias-enhanced Bayesian inference algorithm, which accounts for the intrinsic model deficiency, Polynomial Chaos Expansion to accelerate model evaluation and Markov Chain Monte Carlo sampling, and Karhunen-Lo %60 eve (KL) Expansion to reduce the dimensionality of the state space. We have established an atmospheric measurement site in Livermore, CA and are collect- ing continuous measurements of CO₂ , CH₄ and other species that are typically co-emitted with these GHGs. Measurements of co-emitted species can assist in attributing the GHGs to different emissions sectors. Automatic calibrations using traceable standards are performed routinely for the gas-phase measurements. We are also collecting standard meteorological data at the Livermore site as well as planetary boundary height measurements using a ceilometer. The location of the measurement site is well suited to sample air transported between the San Francisco Bay area and the California Central Valley.