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Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification 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 flexible 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 quantification, and optimization under uncertainty that provide the foundation for many of Dakota’s iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

Assessment of BQ-9000 Biodiesel Properties for 2020 (CRADA CRD-15-593)

Biodiesel producers in the United States and Canada can voluntarily participate in the industry's BQ-9000 quality assurance program. This is the fourth in a series of reports documenting biodiesel quality from participating producers. Participants in the BQ-9000 program were requested to voluntarily provide data to a third-party team. This team anonymized and randomized the data prior to providing to the National Renewable Energy Laboratory (NREL) for analysis and reporting. The critical quality parameters analyzed are: sodium and potassium, calcium and magnesium, phosphorus, flash point and alcohol control, water and sediment, cloud point, acid number, free and total glycerin, monoglycerides, sulfur, oxidation stability, and cold soak filterability test (CSFT). The statistical analysis for these parameters is presented in Table ES-1.

09 BIOMASS FUELS↗

Concentration fluctuations and flammability of cryo-compressed hydrogen and methane jets

Compressed hydrogen stored at cryogenic temperatures has a much higher density than room-temperature storage, which enables large-scale hydrogen storage and transport. An understanding of the release of cryogenic hydrogen from pressurized vessels is needed to evaluate the risk and safety concerns with the use of this fuel. Here, the present work extends the analysis of previous experimental studies that measured the gas concentrations of cryo-compressed hydrogen jets and methane jets using a laser Raman scattering diagnostic system. Since the Raman signals are very small, a denoising algorithm was applied to significantly reduce the noise to enable statistical analysis of the data. The transient features of the turbulent jets were characterized by their concentration intermittencies and probability density functions (PDFs). A two-part PDF was developed to predict the bimodal features of the jet concentration distributions. Then, the flammability factors of the cryogenic jets were calculated based on the intermittency and the PDF.

33 ADVANCED PROPULSION SYSTEMS↗

Transboundary determinants of avian zoonotic infectious diseases: challenges for strengthening research capacity and connecting surveillance networks

As the climate changes, global systems have become increasingly unstable and unpredictable. This is particularly true for many disease systems, including subtypes of highly pathogenic avian influenzas (HPAIs) that are circulating the world. Ecological patterns once thought stable are changing, bringing new populations and organisms into contact with one another. Wild birds continue to be hosts and reservoirs for numerous zoonotic pathogens, and strains of HPAI and other pathogens have been introduced into new regions via migrating birds and transboundary trade of wild birds. With these expanding environmental changes, it is even more crucial that regions or counties that previously did not have surveillance programs develop the appropriate skills to sample wild birds and add to the understanding of pathogens in migratory and breeding birds through research. For example, little is known about wild bird infectious diseases and migration along the Mediterranean and Black Sea Flyway (MBSF), which connects Europe, Asia, and Africa. Focusing on avian influenza and the microbiome in migratory wild birds along the MBSF, this project seeks to understand the determinants of transboundary disease propagation and coinfection in regions that are connected by this flyway. Through the creation of a threat reduction network for avian diseases (Avian Zoonotic Disease Network, AZDN) in three countries along the MBSF (Georgia, Ukraine, and Jordan), this project is strengthening capacities for disease diagnostics; microbiomes; ecoimmunology; field biosafety; proper wildlife capture and handling; experimental design; statistical analysis; and vector sampling and biology. Here, we cover what is required to build a wild bird infectious disease research and surveillance program, which includes learning skills in proper bird capture and handling; biosafety and biosecurity; permits; next generation sequencing; leading-edge bioinformatics and statistical analyses; and vector and environmental sampling. Creating connected networks for avian influenzas and other pathogen surveillance will increase coordination and strengthen biosurveillance globally in wild birds.

54 ENVIRONMENTAL SCIENCES↗

Hybrid Simulation of Proton Cyclotron Waves Upstream of Mars Generated by Pickup Ion Beam Distribution

Linear instability analysis as well as a corresponding two‐dimensional hybrid simulation are performed to examine the excitation of the proton cyclotron waves observed upstream of Mars. The waves are believed to be excited by the pickup ions produced from the ionization of the Martian hydrogen exosphere. And previous statistical analysis of wave observations suggested that the waves are mostly related to pickup ion beam velocity distributions. While earlier linear instability analysis of pickup ion beam distributions has mainly been focused on the parallel unstable modes, our analysis reveals that the maximum growth rate occurs at very oblique propagation. The corresponding hybrid simulation confirms the linear analysis results and further demonstrates that the pickup ions are scattered toward an isotropic shell velocity distribution by the waves excited. Interestingly, the waves at oblique propagation gradually damp out and the system is eventually dominated by waves of quasi‐parallel propagation.

79 ASTRONOMY AND ASTROPHYSICS↗

Comparison of SUSY spectra generators for natural SUSY and string landscape predictions

Models of natural supersymmetry give rise to a weak scale m weak ~ m W,Z,h ~ 100 GeV without any (implausible) finetuning of independent contributions to the weak scale. These models, which exhibit radiatively driven naturalness (RNS), are expected to arise from statistical analysis of the string landscape wherein large soft terms are favored, but subject to a not-too-large value of the derived weak scale in each pocket universe of the greater multiverse. The string landscape picture then predicts, using the Isajet SUSY spectra generator Isasugra, a statistical peak at m h ~ 125 GeV with sparticles generally beyond current LHC search limits. In this paper, we investigate how well these conclusions hold up using other popular spectra generators: SOFTSUSY, SPHENO and SUSPECT (SSS). We built a computer code DEW4SLHA which operates on SUSY Les Houches Accord files to calculate the associated electroweak naturalness measure Δ EW . The SSS generators tend to yield a Higgs mass peak ~125–127 GeV with a superparticle mass spectra rather similar to that generated by Isasugra. In an Appendix, we include loop corrections to Δ EW in a more standard notation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On the measurement of shape: With applications to lunar regolith

With the renewed commitment from NASA and other commercial entities for a presence on the Moon, the importance of understanding the characteristics of lunar regolith and how to utilize it have become the target of increasing scrutiny. Much of what is known about lunar regolith was collected during and immediately after the Apollo program, however, analytical techniques and instrumentation have advanced in leaps and bounds in the subsequent decades. Specifically, dynamic image analysis systems have advanced to the point that millions of particles can have morphological characteristics automatically determined in relatively short time frames. Particle morphological data was collected on several lunar samples and a pair of widely used regolith simulants to ascertain the accuracy of these simulants and to explore statistical analysis methods of these large datasets. It is found that these morphology datasets can vary widely depending on the particle size of the particles, and simple averaging of the data skews the results heavily towards the numerically abundant size ranges, the fines. Different reporting methods are suggested to ameliorate these problems. When applied to the lunar regolith, the particles are noted to be less morphologically complex than initially suspected. Compared to the lunar material, the simulants are found to contain some more morphological variability and angular grains. Such difference is likely due to the wildly different comminution processes that these different powder systems are subjected to.

2D shape↗

Detection of Extreme Phenomena in the Stable Boundary Layer over the Amazonian Forest

We apply different methods for detection of extreme phenomena (EP) in air-turbulent time series measured in the nocturnal boundary layer above the Amazon forest. The methods used were: (a) a Morlet complex wavelet transform, which is often used in analysis of non-linear application processes. Through the use of the wavelet, it is possible to observe a phase singularity that involves a strong interaction between an extensive range of scales; (b) recurrence plot tests, which were used to identify a sudden change between different stable atmospheric states. (c) statistical analysis of early-warning signals, which verify simultaneous increases in the autocorrelation function and in the variance in the state variable; and (d) analysis of wind speed versus turbulent kinetic energy to identify different turbulent regimes in the stable boundary layer. We found it is adequate to use a threshold to classify the cases of strong turbulence regime, as a result of the occurrence of EP in the tropical atmosphere. All methods used corroborate and indicate synergy between events that culminate in what we classify as EP of the stable boundary layer above the tropical forest.

54 ENVIRONMENTAL SCIENCES↗

Parameter estimation for X-ray scattering analysis with Hamiltonian Markov Chain Monte Carlo

Bayesian-inference-based approaches, in particular the random-walk Markov Chain Monte Carlo (MCMC) method, have received much attention recently for X-ray scattering analysis. Hamiltonian MCMC, a state-of-the-art development in the field of MCMC, has become popular in recent years. It utilizes Hamiltonian dynamics for indirect but much more efficient drawings of the model parameters. We described the principle of the Hamiltonian MCMC for inversion problems in X-ray scattering analysis by estimating high-dimensional models for several motivating scenarios in small-angle X-ray scattering, reflectivity, and X-ray fluorescence holography. Hamiltonian MCMC with appropriate preconditioning can deliver superior performance over the random-walk MCMC, and thus can be used as an efficient tool for the statistical analysis of the parameter distributions, as well as model predictions and confidence analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hauser-Feshbach Analysis of Fast Neutron-Induced Reactions on Chlorine

Neutron-induced reactions on 35Cl have recently been measured and analyzed in a Hauser-Feshbach framework at Los Alamos National Laboratory. Particular focus has been applied to the “fast” energy range above 100 keV, where these reactions become important for applications like CLYC (Cs 2 LiYCl 6 :Ce) detector characterization and the development of molten chloride fast reactors. However, challenges to applying a purely statistical analysis to this mass range have presented themselves in the form of cross section fluctuations and deviations due to low-mass structure. In this paper, these challenges and their current solutions will be highlighted, as well as preliminary extensions of the analysis to neighboring isotopes and future plans to extend the measurements down to thermal energies.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

A Framework Using Applied Process Analysis Methods to Assess Water Security in the Vu Gia–Thu Bon River Basin, Vietnam

The Vu Gia–Thu Bon (VG–TB) river basin is facing numerous challenges to water security, particularly in light of the increasing impacts of climate change. These challenges, including salinity intrusion, shifts in rainfall patterns, and reduced water supply in downstream areas, are of great concern. This study comprehensively assessed the current state of water security in the basin using robust statistical analysis methods such as the Process Analysis Method (PAM), SMART principle, and Analytic Hierarchy Process (AHP). This resulted in the development of a comprehensive assessment framework for water security in the VG–TB river basin. This framework identified five key dimensions, with basin development activities (0.32), the ability to meet water needs (0.24), and natural disaster resilience (0.19) being the most crucial and water resource potential being the least crucial (0.11) according to the AHP methodology. The latter also highlighted 15 indicators, four of which are particularly influential, including waste resources (0.54), flood (0.53), water storage capacity (0.45), and basin governance (0.42). Furthermore, 28 variables with high weight factors were identified. This framework aligns with the UN-Water water security definition and addresses the global water sustainability criteria outlined in Sustainable Development Goal 6 (SDG6). It enables the computation of a comprehensive Water Security Index (WSI) for specific regions, providing a strong foundation for decision-making and policy formulation. It aims to enhance water security in the context of climate change and support sustainable basin development, thereby guiding future research and policy decisions in water resource management.

54 ENVIRONMENTAL SCIENCES↗

Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.

97 MATHEMATICS AND COMPUTING↗

A hybrid data–model approach to map soil thickness in mountain hillslopes

Abstract. Soil thickness plays a central role in the interactions between vegetation, soils, and topography, where it controls the retention and release of water, carbon, nitrogen, and metals. However, mapping soil thickness, here defined as the mobile regolith layer, at high spatial resolution remains challenging. Here, we develop a hybrid model that combines a process-based model and empirical relationships to estimate the spatial heterogeneity of soil thickness with fine spatial resolution (0.5 m). We apply this model to two aspects of hillslopes (southwest- and northeast-facing, respectively) in the East River watershed in Colorado. Two independent measurement methods – auger and cone penetrometer – are used to sample soil thickness at 78 locations to calibrate the local value of unconstrained parameters within the hybrid model. Sensitivity analysis using the hybrid model reveals that the diffusion coefficient used in hillslope diffusion modeling has the largest sensitivity among all input parameters. In addition, our results from both sampling and modeling show that, in general, the northeast-facing hillslope has a deeper soil layer than the southwest-facing hillslope. By comparing the soil thickness estimated between a machine-learning approach and this hybrid model, the hybrid model provides higher accuracy and requires less sampling data. Modeling results further reveal that the southwest-facing hillslope has a slightly faster surface soil erosion rate and soil production rate than the northeast-facing hillslope, which suggests that the relatively less dense vegetation cover and drier surface soils on the southwest-facing slopes influence soil properties. With seven parameters in total for calibration, this hybrid model can provide a realistic soil thickness map with a relatively small amount of sampling dataset comparing to machine-learning approach. Integrating process-based modeling and statistical analysis not only provides a thorough understanding of the fundamental mechanisms for soil thickness prediction but also integrates the strengths of both statistical approaches and process-based modeling approaches.

58 GEOSCIENCES↗

Machine learning insights into microstructural origins of transport and mechanical properties in porous microstructures

Multifunctional porous materials are increasingly needed across various fields, but their complex microstructures create significant challenges due to the intricate microstructure-property relationships. This complexity, combined with limitations of traditional analysis methods, hinders efforts to understand and optimize microstructure–property relationships. Here, to address this, we integrate physics-based mesoscale modeling with interpretable machine learning (ML) to uncover how microstructural features govern effective diffusivity and elastic modulus. At constant porosity, we show diffusivity varies by over 150 × and modulus by ∼50 ×, highlighting the power of microstructure engineering. Statistical analysis reveals bimodal behavior in diffusivity and unimodal in modulus. ML identifies connectivity as the dominant factor, while modulus is also sensitive to domain size and feature interactions. Controlled simulations further highlight domain shape as a critical feature for modulus. This framework enables efficient exploration of microstructure-property correlations, offering new insights to guide the design of advanced porous materials.

Bicontinuous microstructure↗

Monte–Carlo ray-tracing studies of multiplexed prismatic graphite analyzers for the cold-neutron triple-axis spectrometer at the High Flux Isotope Reactor

A modern cold triple-axis spectrometer to study quantum condensed matter systems is planned for the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. Here, we describe the conceptual principles and design of a secondary spectrometer using a multiplexed, prismatic analyzer system relying on graphite crystals and inspired by the successful implementation of the Continuous Angle Multiple Energy Analysis (CAMEA) spectrometers at the Paul Scherrer Institute. This project is currently known as MANTA for Multi-Analyzer Neutron Triple-Axis. Here, we report Monte-Carlo ray-tracing simulations on a simple but realistic sample scattering kernel to further illustrate the prismatic analyzer concept’s workings, calibration, and performance. Then, we introduce a new statistical analysis approach based on the prismatic analyzer concept to improve the number of final energies measured on the spectrometer. We also study possible evolutions in the CAMEA design relevant for MANTA.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Major to trace element imaging and analysis of iron age glasses using stage scanning in the analytical dual beam microscope (tandem)

Dark and clear silicate glasses formed during an iron age vitrification event ≈ 1500 years ago at the Broborg hillfort near Uppsala, Sweden have been analyzed using a scanning electron microscope equipped with a micro-X-ray fluorescence (μXRF) spectrometer. Correlated µXRF and electron beam-induced energy dispersive spectrometry (EDS) X-ray maps were collected via stage-scanning at constant velocity. This coupled procedure represents a new approach for the cultural heritage community to conduct analytical studies of archaeometric specimens composed of metal, ceramic, or mixed inorganic/organic materials, where major and trace element compositions are registered in space for areas up to the centimeter-length scale at micrometer-scale resolution. Overview images were used to select areas for EDS beam scan maps correlated with multispectral cathodoluminescence (CL) imaging and co-located quantitative EDS and μXRF point analysis. Fe, Ca, Mg, Ti, P, Mn, Zr, Zn, and Y are enriched in the dark glass, while Si, Al, K, Na, Ba, Sr, Rb, and Ga are enriched in the clear glass. Unmelted material is comprised predominately of quartz (SiO 2 ) along with trace apatite (Ca 5 (PO 4 ) 3 [Cl,OH]) and zircon (ZrSiO 4 ). Multivariate statistical analysis was used to measure the area fractions of high variance components while lower variance components represented phase mixtures. Differences between calculated melt viscosities for the glass compositions are consistent with field and laboratory observations. Coupled large area EDS and μXRF imaging shows significant promise for informed selection of higher spatial resolution and higher sensitivity follow-up studies, e.g., those performed using synchrotron analysis.

36 MATERIALS SCIENCE↗

Towards a Comparative Assessment of Data-Driven Process Models in Health Information Technology

Process mining for conformance analysis focuses on comparing a reference process model against a data-driven process model that is generated via log files from information technology systems. While this approach is helpful when there is an existing process model in an organization, it leaves the question of what to do in the absence of a complete reference process model unanswered. In this paper, we present a comparative assessment approach that combines process mining, process mapping for dimensionality reduction, and statistical analysis. Our goal is to find similarities and dissimilarities in data-driven process models among U.S. Veterans Health Administration (VHA) facilities to assess process conformance among different healthcare facilities, which can help assess the standardization of care. We illustrate our approach by applying it to two clinical radiology order process models generated by two similar facilities. Our results demonstrate statistical similarities in the standardization of care among those two facilities.

Klasky, Hilda↗