Publications

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This paper supports a special session on "Frontiers of Uncertainty Management for Com- plex Aerospace Systems" with the intent of summarizing two aspects of the DOE/NNSA Accelerated Strategic Computing (ASC) program, each of which is focused on predictive science using complex simulation models. The first aspect is academic outreach, as enabled by the Predictive Science Academic Alliance Program (PSAAP). The second aspect is the Dakota project at Sandia National Laboratories, which develops and deploys uncertainty quantification capabilities focused on high fidelity modeling and simulation on large-scale parallel computers.

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 report summarizes the result of a NEAMS project focused on sensitivity analysis of the heat transfer model in the gap between the fuel rod and the cladding used in the BISON fuel performance code of Idaho National Laboratory. Using the gap heat transfer models in BISON, the sensitivity of the modeling parameters and the associated responses is investigated. The study results in a quantitative assessment of the role of various parameters in the analysis of gap heat transfer in nuclear fuel.

This report summarizes the result of LDRD project 12-0395, titled "Automated Algorithms for Quantum-level Accuracy in Atomistic Simulations." During the course of this LDRD, we have developed an interatomic potential for solids and liquids called Spectral Neighbor Analysis Poten- tial (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected on to a basis of hyperspherical harmonics in four dimensions. The SNAP coef- ficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. Global optimization methods in the DAKOTA software package are used to seek out good choices of hyperparameters that define the overall structure of the SNAP potential. FitSnap.py, a Python-based software pack- age interfacing to both LAMMPS and DAKOTA is used to formulate the linear regression problem, solve it, and analyze the accuracy of the resultant SNAP potential. We describe a SNAP potential for tantalum that accurately reproduces a variety of solid and liquid properties. Most significantly, in contrast to existing tantalum potentials, SNAP correctly predicts the Peierls barrier for screw dislocation motion. We also present results from SNAP potentials generated for indium phosphide (InP) and silica (SiO 2 ). We describe efficient algorithms for calculating SNAP forces and energies in molecular dynamics simulations using massively parallel computers and advanced processor ar- chitectures. Finally, we briefly describe the MSM method for efficient calculation of electrostatic interactions on massively parallel computers.

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quanti cation, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

In the past several years, several international agencies have begun to collect data on human performance in nuclear power plant simulators [1]. This data provides a valuable opportunity to improve human reliability analysis (HRA), but there improvements will not be realized without implementation of Bayesian methods. Bayesian methods are widely used in to incorporate sparse data into models in many parts of probabilistic risk assessment (PRA), but Bayesian methods have not been adopted by the HRA community. In this article, we provide a Bayesian methodology to formally use simulator data to refine the human error probabilities (HEPs) assigned by existing HRA methods. We demonstrate the methodology with a case study, wherein we use simulator data from the Halden Reactor Project to update the probability assignments from the SPAR-H method. The case study demonstrates the ability to use performance data, even sparse data, to improve existing HRA methods. Furthermore, this paper also serves as a demonstration of the value of Bayesian methods to improve the technical basis of HRA.

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One objective of the Climate Science for a Sustainable Energy Future (CSSEF) program is to develop the capability to thoroughly test and understand the uncertainties in the overall climate model and its components as they are being developed. The focus on uncertainties involves sensitivity analysis: the capability to determine which input parameters have a major influence on the output responses of interest. This report presents some initial sensitivity analysis results performed by Lawrence Livermore National Laboratory (LNNL), Sandia National Laboratories (SNL), and Pacific Northwest National Laboratory (PNNL). In the 2011-2012 timeframe, these laboratories worked in collaboration to perform sensitivity analyses of a set of CAM5, 2° runs, where the response metrics of interest were precipitation metrics. The three labs performed their sensitivity analysis (SA) studies separately and then compared results. Overall, the results were quite consistent with each other although the methods used were different. This exercise provided a robustness check of the global sensitivity analysis metrics and identified some strongly influential parameters.

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We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural error in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.

Large-scale computational models have become common tools for analyzing complex man-made systems. However, when coupled with optimization or uncertainty quantification methods in order to conduct extensive model exploration and analysis, the computational expense quickly becomes intractable. Furthermore, these models may have both continuous and discrete parameters. One common approach to mitigating the computational expense is the use of response surface approximations. While well developed for models with continuous parameters, they are still new and largely untested for models with both continuous and discrete parameters. In this work, we describe and investigate the performance of three types of response surfaces developed for mixed-variable models: Adaptive Component Selection and Shrinkage Operator, Treed Gaussian Process, and Gaussian Process with Special Correlation Functions. We focus our efforts on test problems with a small number of parameters of interest, a characteristic of many physics-based engineering models. We present the results of our studies and offer some insights regarding the performance of each response surface approximation method. © 2014 Springer International Publishing Switzerland.

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This report discusses the treatment of uncertainties stemming from relatively few samples of random quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse data samples it is not practical to have a goal of accurately estimating the underlying probability density function (PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a specified percentile range of the actual PDF, say the range between 0.025 and .975 percentiles, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the desired percentile range of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem interesting and difficult. In this report, five uncertainty representation techniques are characterized for their performance on twenty-one test problems (over thousands of trials for each problem) according to these two opposing objectives and other performance measures. Two of the methods, statistical Tolerance Intervals and a kernel density approach specifically developed for handling sparse data, exhibit significantly better overall performance than the others.

This report summarizes the result of a NEAMS project focused on the use of reliability methods within the RAVEN and RELAP-7 software framework for assessing failure probabilities as part of probabilistic risk assessment for nuclear power plants. RAVEN is a software tool under development at the Idaho National Laboratory that acts as the control logic driver and post-processing tool for the newly developed Thermal-Hydraulic code RELAP-7. Dakota is a software tool developed at Sandia National Laboratories containing optimization, sensitivity analysis, and uncertainty quantification algorithms. Reliability methods are algorithms which transform the uncertainty problem to an optimization problem to solve for the failure probability, given uncertainty on problem inputs and a failure threshold on an output response. The goal of this work is to demonstrate the use of reliability methods in Dakota with RAVEN/RELAP-7. These capabilities are demonstrated on a demonstration of a Station Blackout analysis of a simplified Pressurized Water Reactor (PWR).