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UQTk (V. 3.0) User Manual

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

97 MATHEMATICS AND COMPUTING↗

UQTk User Manual (V.3.1.0)

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.0 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

97 MATHEMATICS AND COMPUTING↗

UQTk Version 3.1.1 User Manual

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.1 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

97 MATHEMATICS AND COMPUTING↗

UQTk Version 3.0.4 User Manual

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0.4 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

97 MATHEMATICS AND COMPUTING↗

UQTk Version 3.1.2 User Manual

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.2 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

97 MATHEMATICS AND COMPUTING↗

Luminous Infrared Galaxies with the Submillimeter Array. V. Molecular Gas in Intermediate to Late-stage Mergers

We present new high-resolution ALMA ({sup 13}CO J = 1−0 and J = 2−1) and CARMA ({sup 12}CO and {sup 13}CO J = 1−0) observations of two luminous infrared galaxies (LIRGs), Arp 55 and NGC 2623. The new data are complementary to published and archival submillimeter array observations of {sup 12}CO J = 2−1 and J = 3−2. We perform a Bayesian likelihood non-local thermodynamic equilibrium analysis to constrain the molecular gas physical conditions such as temperature, column, and volume densities and the [{sup 12}CO]/[{sup 13}CO] abundance ratio. For Arp 55, an early/intermediate-staged merger, the line measurements are consistent with cold (∼10–20 K), dense (>10{sup 3.5} cm{sup −3}) molecular gas. For NGC 2623, the molecular gas is warmer (∼110 K) and less dense (∼10{sup 2.7} cm{sup −3}). Because Arp 55 is an early/intermediate stage merger, while NGC 2623 is a merger remnant, the difference in physical conditions may be an indicator of merger stage. Comparing the temperature and volume density of several LIRGs shows that the molecular gas, averaged over ∼kiloparsec scales, of advanced mergers is in general warmer and less dense than early/intermediate stage mergers. We also find that the [{sup 12}CO]/[{sup 13}CO] abundance ratio of NGC 2623 is unusually high (>250) when compared with the Milky Way; however, it follows a trend seen with other LIRGs in the literature. This high [{sup 12}CO]/[{sup 13}CO] value is very likely due to stellar nucleosynthesis enrichment of the interstellar medium. On the other hand, Arp 55 has a more Galactic [{sup 12}CO]/[{sup 13}CO] value with the most probable [{sup 12}CO]/[{sup 13}CO] value being 20–30. We measure the CO-to-H{sub 2} conversion factor, α{sub CO}, to be ∼0.1 and ∼0.7 (3 × 10{sup −4}/x{sub CO}) M {sub ⊙} (K km s{sup −1} pc{sup 2}){sup −1} for Arp 55 and NGC 2623, respectively. Because Arp 55 is an early/intermediate-stage merger, this suggests that the transition from a Galactic conversion factor to a LIRG value happens at an even earlier merger stage.

79 ASTRONOMY AND ASTROPHYSICS↗

A novel application of cosmic rays for spent nuclear fuel monitoring - 15738

Monitoring nuclear waste and controlling spent nuclear fuel at its source is one of the main strategies to minimize the risks of nuclear proliferation and reduce potential homeland threats. Storage of high level waste from a fission reactor typically involves placing spent fuel in sealed dry casks. After the spent nuclear fuel has been placed inside the dry cask, the cask is welded, not allowing for visual inspection. Conventional methods for examining the interior of materials e.g., X-rays, are limited by the fact that they cannot penetrate very dense well-shielded objects. Instead, cosmic ray muons have the potential to allow for assessment of spent nuclear fuel stored within sealed dense dry casks. Objectives: 1.Exploit the ability of cosmic ray muons to penetrate high density materials allowing the distribution of materials within the object to be inferred from the muon tracks. 2. Develop a monitoring system that tracks the path of cosmic ray muons, including their deflection and attenuation, to identify the contents of a closed dry cask. Methods: - Monte-Carlo simulations using Geant4; - Bayesian decision theory for signal classification; - Wavelet analysis for noise cancellation; - Chaotic Neural Networks for signal encryption. Results: 1. Preliminary statistical analysis proved that the method is feasible and has the ability to identify the presence of spent nuclear fuel in a dry cask. 2. Using monoenergetic muons, a dry cask with one fuel assembly missing can be correctly identified with error rate <1%. Broader merit: Once completed, the proposed project for cosmic ray muon transport will enable a new and potentially transformative approach towards efficient, inexpensive and remote cosmic ray muon applications in archaeology, medicine and safeguarding of nuclear materials.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Bayesian classification of falls risk

Background. Prior research in falls risk prediction often relies on qualitative and/or clinical methods. There are two challenges with these methods. First, qualitative methods typically use falls history to determine falls risk. Second, clinical methods do not quantify the uncertainty in the classification decision. In this paper, we propose using Bayesian classification to predict falls risk using vectors of gait variables shown to contribute to falls risk. Research Questions: (1) Using a vector of risk ratios for specific gait variables shown to contribute to falls risk, how can older adults be classified as low or high falls risk? and (2) how can the uncertainty in the classifier decision be quantified when using a vector of gait variables? Methods. Using a pressure sensitive walkway, biomechanical measurements of gait were collected from 854 adults over the age of 65. In our method, we first determine low and high falls risk labels for vectors of risk ratios using the k-means algorithm. Next, the posterior probability of low or high falls risk class membership is obtained from a two component Gaussian mixture model (GMM) of gait vectors, which enables risk assessment directly from the underlying biomechanics. We classify the gait vectors using a threshold based on Youden's J statistic. Results. Through a Monte Carlo simulation and an analysis of the receiver operating characteristic (ROC), we demonstrate that our Bayesian classifier, when compared to the k-means falls risk labels, achieves an accuracy greater than 96% at predicting low or high falls risk. Significance. Our analysis indicates that our approach based on a Bayesian framework and an individual's underlying biomechanics can predict falls risk while quantifying uncertainty in the classification decision.

59 BASIC BIOLOGICAL SCIENCES↗

Practical Use of Computationally Frugal Model Analysis Methods

Computationally frugal methods of model analysis can provide substantial benefits when developing models of groundwater and other environmental systems. Model analysis includes ways to evaluate model adequacy and to perform sensitivity and uncertainty analysis. Frugal methods typically require 10s of parallelizable model runs; their convenience allows for other uses of the computational effort. We suggest that model analysis be posed as a set of questions used to organize methods that range from frugal to expensive (requiring 10,000 model runs or more). This encourages focus on method utility, even when methods have starkly different theoretical backgrounds. We note that many frugal methods are more useful when unrealistic process-model nonlinearities are reduced. Inexpensive diagnostics are identified for determining when frugal methods are advantageous. Examples from the literature are used to demonstrate local methods and the diagnostics. We suggest that the greater use of computationally frugal model analysis methods would allow questions such as those posed in this work to be addressed more routinely, allowing the environmental sciences community to obtain greater scientific insight from the many ongoing and future modeling efforts

54 ENVIRONMENTAL SCIENCES↗

High-energy-density-physics measurements in implosions using Bayesian inference

Convergent high-energy-density (HED) experimental platforms are used to study matter under some of the most extreme conditions that can be produced on Earth, comparable to the interior of stars. There are many challenges in using these systems for fundamental measurements currently being addressed by new analysis methods, such as the combination of a reduced physics model and Bayesian inference, allowing a self-consistent inference of physical quantities with a robust error analysis. These methods in combination with simple (as compared to inertial confinement fusion implosions) implosion platforms, which can be modified to show sensitivity to different physical mechanisms of interest, are used to study the physical properties of matter under extreme conditions. This work discusses a subset of implosion targets for studying opacity effects, electron-ion equilibration, and thermal conductivity and, as an example, a system consisting of a thick-shelled, gas-filled laser-direct-drive implosion is used to show how a reduced model and Bayesian inference can help inform experimental design decisions such as diagnostic choice. It is shown that for this system that a combination of neutron and x-ray self-emission diagnostics is critical for constraining the details of the thermodynamic states in the system and that the conductivity exponent in a Spitzer like framework can be constrained to the 30% level in deuterium at gigabar conditions. Furthermore, this process can be applied to many HED systems to make underlying model assumptions explicit and facilitate experimental design and analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Sensitivity Analysis of Genome-Scale Metabolic Flux Prediction

TRIMER, Transcription Regulation Integrated with MEtabolic Regulation, is a genome-scale modeling pipeline targeting at metabolic engineering applications. Using TRIMER, regulated metabolic reactions can be effectively predicted by integrative modeling of metabolic reactions with a Transcription Factor (TF)-gene regulatory network (TRN), which is modeled via a Bayesian network (BN). In this paper, we focus on sensitivity analysis of metabolic flux prediction for uncertainty quantification of BN structures for TRN modeling in TRIMER. We propose a computational strategy to construct the uncertainty class of TRN models based on the inferred regulatory order uncertainty given transcriptomic expression data. With that, we analyze the prediction sensitivity of the TRIMER pipeline for the metabolite yields of interest. The obtained sensitivity analyses can guide Optimal Experimental Design (OED) to help acquire new data that can enhance TRN modeling and achieve specific metabolic engineering objectives, including metabolite yield alterations. Here we have performed small- and large-scale simulated experiments, demonstrating the effectiveness of our developed sensitivity analysis strategy for BN structure learning to quantify the edge importance in terms of metabolic flux prediction uncertainty reduction and its potential to effectively guide OED.

59 BASIC BIOLOGICAL SCIENCES↗

A Bayesian approach to evaluation of soil biogeochemical models

Abstract. To make predictions about the carbon cycling consequences of rising global surface temperatures, Earth system scientists rely on mathematical soil biogeochemical models (SBMs). However, it is not clear which models have better predictive accuracy, and a rigorous quantitative approach for comparing and validating the predictions has yet to be established. In this study, we present a Bayesian approach to SBM comparison that can be incorporated into a statistical model selection framework. We compared the fits of linear and nonlinear SBMs to soil respiration data compiled in a recent meta-analysis of soil warming field experiments. Fit quality was quantified using Bayesian goodness-of-fit metrics, including the widely applicable information criterion (WAIC) and leave-one-out cross validation (LOO). We found that the linear model generally outperformed the nonlinear model at fitting the meta-analysis data set. Both WAIC and LOO computed higher overfitting risk and effective numbers of parameters for the nonlinear model compared to the linear model, conditional on the data set. Goodness of fit for both models generally improved when they were initialized with lower and more realistic steady-state soil organic carbon densities. Still, testing whether linear models offer definitively superior predictive performance over nonlinear models on a global scale will require comparisons with additional site-specific data sets of suitable size and dimensionality. Such comparisons can build upon the approach defined in this study to make more rigorous statistical determinations about model accuracy while leveraging emerging data sets, such as those from long-term ecological research experiments.

54 ENVIRONMENTAL SCIENCES↗

Impact of Trucking Network Flow on Preferred Biorefinery Locations in the Southern United States

The impact of the trucking transportation network flow was modeled for the southern United States. The study addresses a gap in existing research by applying a Bayesian logistic regression and Geographic Information System (GIS) geospatial analysis to predict biorefinery site locations. A one-way trucking cost assuming a 128.8 km (80-mile) haul distance was estimated by the Biomass Site Assessment model. The “median family income,” “timberland annual growth-to-removal ratio,” and “transportation delays” were significant in determining mill location. Transportation delays that directly impacted the costs of trucking are presented. Here, a logistic model with Bayesian inference was used to identify preferred site locations, and locations not preferential for a mill location. The model predicted that higher probability locations for smaller biomass mills (feedstock capacity, the size of sawmills) were in southern Alabama, southern Georgia, southeast Mississippi, southern Virginia, western Louisiana, western Arkansas, and eastern Texas. The higher probability locations for large capacity mills (feedstock capacity, the size for pulp and paper mills) were in southeastern Alabama, southern Georgia, central North Carolina, and the Mississippi Delta regions.

09 BIOMASS FUELS↗

How data science methods can improve the quality and efficiency of ICF and HEDP research

Data Science methods (many that are Bayesian based) are widely used in the physical sciences to estimate model parameters from experimental data, synthesize heterogeneous data, calibrate models, design experiments, and determine statistical significance of data. These methods provide a wealth of advantages over traditional analysis techniques because: 1) uncertainties are rigorously defined and propagated naturally through complex systems including covariance, 2) prior information is captured within the analysis framework (including rad-MHD and rad-hydro simulations), 3) competing models can be selected and/or ruled out using quantitative criteria, and 4) complex, heterogeneous data can be incorporated simultaneously. While these methods have been widely adopted as the gold standard in fields such as particle physics, astronomy, and biology, they have been slow to catch on in Inertial Confinement Fusion (ICF) and High Energy Density Physics (HEDP) research. Recently, several teams at LLNL, SNL, LANL, and the LLE have been exploring the use of these tools in their research and have found success. Here we propose that a concerted effort to consolidate these independent research efforts by developing and deploying common tools for use across the complex can revolutionize the way we approach data analysis, assimilation of theory and experiment, and decision making. The Bayesian formalism provides a means to accomplish this, but we are lacking certain infrastructure to make it happen on a large scale. Furthermore, once adopted, these techniques can be used to develop standards by which discoveries can be judged, similar to the so-called 5σ rule in high energy particle physics. Such standards may be used in the future to address the issue of unknown reproducibility in ICF and HED experiments caused by low shot rate and high cost per experiment. Our goals as a group are to advance the state of the art in HED measurement science by enabling: 1) better inferences from data with well-defined uncertainties, 2) better use of the data we have and continue to collect, 3) intelligent synthesis of data, 4) evaluation of the statistical significance of our data, and 5) informed decision making regarding the design of new experiments and instruments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A framework for assessment of predictive capability maturity and its application in nuclear thermal hydraulics

Here this work presents a formalized and computerized framework for the assessment of decision regarding the adequacy of a simulation tool for a nuclear reactor application. The decision regarding a code’s adequacy for an application is dependent on the assessment of different attributes that govern verification, validation, and uncertainty quantification of the code. In this work, the focus is on code validation. Therefore, the framework is developed and illustrated from the perspective of decision regarding the validation assessment of a code. Code validation assessment is performed based on the validation test results, data applicability, and process quality assurance factors. The process quality assurance factors warrant the trustworthiness of the evidence and help in checking people and process compliance with respect to the standard requirements. The proposed framework is developed using an argument modeling technique called Goal Structuring Notation (GSN). Goal structuring notation facilitates structural knowledge representation, information abstraction, evidence incorporation, and provides a skeletal structure for quantitative maturity assessment. The decision schema for the development of the decision model is based on the Predictive Capability Maturity Model (PCMM) and Analytic Hierarchy Process (AHP) and formalized using Goal structuring notation. Each decision attribute is formulated as a claim, where the degree of validity of the claim (attribute’s assessment) is expressed using different maturity levels. The GSN representation of the decision model is transformed into a confidence network to provide evidence-based quantitative maturity assessment using the Bayesian network. A metric based on the expected utility of maturity levels, called expected distance metric, is proposed to measure the distance between target maturity and achieved maturity on a scale of zero to one. Expected distance metric helps in comparing the assessment of different attributes and identification of major areas of concern in terms of modeling capability, data needs, and quality of assessment process. The practical application of the framework is demonstrated by a case study on validation assessment of a thermal-hydraulic code for a challenge problem called Departure from Nucleate Boiling (DNB).

42 ENGINEERING↗