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Results for “Bayesian statistical modeling”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Bayesian estimation of the $S$ factor and thermonuclear reaction rate for 16 O(p, γ) 17 F

The 16 O(p, γ) 17 F reaction is the slowest hydrogen-burning process in the CNO mass region. Its thermonuclear rate sensitively impacts predictions of oxygen isotopic ratios in a number of astrophysical sites, including AGB stars. The reaction has been measured several times at low bombarding energies using a variety of techniques. The most recent evaluated experimental rates have a reported uncertainty of about 7.5% below 1 GK. However, the previous rate estimate represents a best guess only and was not based on rigorous statistical methods. We apply a Bayesian model to fit all reliable 16 O(p, γ) 17 F cross section data, and take into account independent contributions of statistical and systematic uncertainties. The nuclear reaction model employed is a single-particle potential model involving a Woods-Saxon potential for generating the radial bound state wave function. The model has three physical parameters, the radius and diffuseness of the Woods-Saxon potential, and the asymptotic normalization coefficients (ANCs) of the final bound state in 17 F. Here, we find that performing the Bayesian S -factor fit using ANCs as scaling parameters has a distinct advantage over adopting spectroscopic factors instead. Based on these results, we present the first statistically rigorous estimation of experimental 16 O(p, γ) 17 F reaction rates, with uncertainties (±4.2%) of about half the previously reported values.

6 ≤ A ≤ 19↗
DOE OSTI2019

A comparison of material flow strength models using Bayesian cross-validation

Predicting material flow strength over a range of conditions, such as temperature and strain rate, is necessary for many engineering applications. In this paper, we consider how to compare the predictiveness of several different strength models using a statistical technique called Bayesian cross-validation. Given a dataset of flow strength measurements obtained from mechanictesting experiments, the procedure consists of performing a Bayesian calibration of each strength model on a subset of the data and evaluating how well the trained models predict the remaining data. The predictiveness of a calibrated strength model is quantifiable probabilistically, which provides an interpretable metric for comparing the different models. As an illustrative example, we compare the Johnson-Cook (JC), Zerilli-Armstrong (ZA), Preston-Tonks-Wallace (PTW), and Mechanical Threshold Stress (MTS) flow strength models for the tantalum stress-strain curve data from Chen and Gray (1996). We show that prediction intervals for the four strength models cover the held-out data at most experimental conditions, but also that prediction interval coverage and prediction uncertainty varies by model and experimental condition. Finally, the analysis further allows us to identify experimental regimes for which one of the strength models predicts better than the other three.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A Bayesian approach to modeling diffraction profiles and application to ferroelectric materials

A new statistical approach for modeling diffraction profiles is introduced, using Bayesian inference and a Markov chain Monte Carlo (MCMC) algorithm. This method is demonstrated by modeling the degenerate reflections during application of an electric field to two different ferroelectric materials: thin-film lead zirconate titanate (PZT) of composition PbZr 0.3 Ti 0.7 O 3 and a bulk commercial PZT polycrystalline ferroelectric. Here, the new method offers a unique uncertainty quantification of the model parameters that can be readily propagated into new calculated parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Sequential Bayesian Parameter Estimation of Stochastic Dynamic Load Models

In this paper we focus on the parameter estimation of dynamic load models with stochastic terms-in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty in the aggregated protection characteristics can be formulated as a stochastic differential equation with process noise. We cast the parameter inversion within a Bayesian parameter estimation framework, and we present methods to include process noise. We demonstrate the benefits of considering stochasticity in the parameter estimation and the risks of ignoring it.

Bayesian Statistics↗
DOE OSTI2015

Uncertainty quantification and propagation in nuclear density functional theory

Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going eff orts seek to better root nuclear DFT in the theory of nuclear forces, energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in fi nite nuclei. In this study, we review recent eff orts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Linking big models to big data: efficient ecosystem model calibration through Bayesian model emulation

Data-model integration plays a critical role in assessing and improving our capacity to predict ecosystem dynamics. Similarly, the ability to attach quantitative statements of uncertainty around model forecasts is crucial for model assessment and interpretation and for setting field research priorities. Bayesian methods provide a rigorous data assimilation framework for these applications, especially for problems with multiple data constraints. However, the Markov chain Monte Carlo (MCMC) techniques underlying most Bayesian calibration can be prohibitive for computationally demanding models and large datasets. We employ an alternative method, Bayesian model emulation of sufficient statistics, that can approximate the full joint posterior density, is more amenable to parallelization, and provides an estimate of parameter sensitivity. Analysis involved informative priors constructed from a meta-analysis of the primary literature and specification of both model and data uncertainties, and it introduced novel approaches to autocorrelation corrections on multiple data streams and emulating the sufficient statistics surface. We report the integration of this method within an ecological workflow management software, Predictive Ecosystem Analyzer (PEcAn), and its application and validation with two process-based terrestrial ecosystem models: SIPNET and ED2. In a test against a synthetic dataset, the emulator was able to retrieve the true parameter values. A comparison of the emulator approach to standard brute-force MCMC involving multiple data constraints showed that the emulator method was able to constrain the faster and simpler SIPNET model's parameters with comparable performance to the brute-force approach but reduced computation time by more than 2 orders of magnitude. The emulator was then applied to calibration of the ED2 model, whose complexity precludes standard (brute-force) Bayesian data assimilation techniques. Both models are constrained after assimilation of the observational data with the emulator method, reducing the uncertainty around their predictions. Performance metrics showed increased agreement between model predictions and data. Our study furthers efforts toward reducing model uncertainties, showing that the emulator method makes it possible to efficiently calibrate complex models.

58 GEOSCIENCES↗
DOE OSTI2021

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Hierarchical Inference of the Lensing Convergence from Photometric Catalogs with Bayesian Graph Neural Networks

Abstract We present a Bayesian graph neural network (BGNN) that can estimate the weak lensing convergence ( κ ) from photometric measurements of galaxies along a given line of sight (LOS). The method is of particular interest in strong gravitational time-delay cosmography (TDC), where characterizing the “external convergence” ( κ ext ) from the lens environment and LOS is necessary for precise Hubble constant ( H 0 ) inference. Starting from a large-scale simulation with a κ resolution of ∼1′, we introduce fluctuations on galaxy–galaxy lensing scales of ∼1″ and extract random sight lines to train our BGNN. We then evaluate the model on test sets with varying degrees of overlap with the training distribution. For each test set of 1000 sight lines, the BGNN infers the individual κ posteriors, which we combine in a hierarchical Bayesian model to yield constraints on the hyperparameters governing the population. For a test field well sampled by the training set, the BGNN recovers the population mean of κ precisely and without bias (within the 2 σ credible interval), resulting in a contribution to the H 0 error budget well under 1%. In the tails of the training set with sparse samples, the BGNN, which can ingest all available information about each sight line, extracts a stronger κ signal compared to a simplified version of the traditional method based on matching galaxy number counts, which is limited by sample variance. Our hierarchical inference pipeline using BGNNs promises to improve the κ ext characterization for precision TDC. The code is available as a public Python package, Node to Joy ⏬ .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Heterogeneous materials and materials with complex microstructures pose a unique challenge in the development of accurate models of their response to external stimuli. These difficulties principally arise due to the difficulty in characterizing and modeling the constituents and their interactions. It is usually possible, though non-trivial, to construct an explicit representation of the microstructure (a direct numeric simulation or DNS) but the method by which the complex modes of deformation and other processes can be homogenized to a reduced-order approximation is frequently unclear. Many homogenization approaches are ad-hoc and lack a strong justification beyond ease of computation. Furthermore, the homogenization approach can, in some cases, not utilize the full breadth of information available in the computation of the macro-scale stresses and deformation measures. It is also noteworthy that homogenization, by its very nature, will tend to obfuscate details of processes occurring at the lower length-scale. It is therefore of interest to include as much information as possible in the construction of the reduced-order model so as to be predictive in a variety of loading environments. We here present a length-scale bridging technique based upon the micromorphic continuum mechanics of Eringen which incorporates volume and surface area averages as a part of its construction. This approach enforces the balance equations at the micro-scale and then studies the effect of the spatially varying nature on the macro-scale. This leads, naturally, to further balance equations which are solved at the macro-scale. This work details a homogenization framework which arises naturally from the micromorphic construction of Eringen attempting to introduce no definitions beyond which are justifiable from micro-structural considerations. One of the results of this effort is the so-called “micromorphic filter” which has been developed and applied to several DNS to demonstrate its effectively. In order to determine the macroscopic degrees of freedom we utilize the special case of an overlap coupling technique where the macro-scale is fully constrained to the micro-scale. This enables us to study the resulting material properties as expected but also allows us to further study the boundary conditions on the additional degrees of freedom at the macro-scale.

42 ENGINEERING↗
DOE OSTI2026

Mass of 101 Sn and Bayesian extrapolations to the proton drip line

The favorable energy configurations of nuclei at magic numbers of 𝑁 neutrons and 𝑍 protons are fundamental for understanding the evolution of nuclear structure. The 𝑍 = 50 (tin) isotopic chain is a frontier for such studies, with particular interest at and around the doubly magic 100 Sn isotope, for which the mass is a topic of debate. Precise mass values for neutron-deficient isotopes provide necessary anchor points for mass models to test extrapolations near the proton drip line, where experimental studies remain out of reach. In this work, we report a Penning trap mass measurement of 101 Sn . The determined mass excess of −59889.89⁢(96) keV for 101 Sn represents a factor-of-300 improvement over the current precision and indicates that 101 Sn is less bound than previously thought. Mass predictions from a recently developed Bayesian model combination framework employing statistical machine learning and nuclear masses computed within seven global models based on nuclear density functional theory agree within 1⁢𝜎 with experimental masses from the 48 ≤ 𝑍 ≤ 52 isotopic chains. The framework's resilience to new mass data gave confidence in the extrapolation of tin masses down to 𝑁 = 46. Our calculations suggest that 96 Sn is a two-proton drip line nucleus and predict a mass excess of −58090⁢(800) keV for 100 Sn , showing a preference within 1⁢𝜎 for the mass of 100 Sn derived from the 𝛽-delayed 𝑄 value measured at GSI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

A NEW REFERENCE CHEMICAL COMPOSITION FOR TMC-1

Recent detections of complex organic molecules in dark clouds have rekindled interest in the astrochemical modeling of these environments. Because of its relative closeness and rich molecular complexity, TMC-1 has been extensively observed to study the chemical processes taking place in dark clouds. We use local thermodynamical equilibrium radiative transfer modeling coupled with a Bayesian statistical method which takes into account outliers to analyze the data from the Nobeyama spectral survey of TMC-1 between 8 and 50 GHz. We compute the abundance relative to molecular hydrogen of 57 molecules, including 19 isotopologues in TMC-1 along with their associated uncertainty. The new results are in general agreement with previous abundance determination from Ohishi and Kaifu and the values reported in the review from Agúndez and Wakelam. However, in some cases, large opacity and low signal to noise effects allow only upper or lower limits to be derived, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Estimating Material Properties Under Extreme Conditions by Using Bayesian Model Calibration with Functional Outputs

Summary Dynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto-correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment-specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A Markov framework for generalized post-event systems recovery modeling: From single to multihazards

State-dependent models can be used to represent the system recovery process as a series of stochastic transitions from lower to higher functional states. However, the applications of these models have been limited in scope and there is a lack of a generalized recovery modeling framework. A generalized framework would permit a robust forecasting of systems and system-of-systems recovery under multiple hazards, and more broadly, would contribute to community disaster preparedness. This paper develops a generalized post hazard-event recovery modeling framework based on state-dependent Markov-type processes. We then apply the proposed framework to solve a spectrum of problems that range from hind-casting single-system recovery following a single hazard event to forecasting post-event trajectories under multiple hazards and modeling the recovery of a system-of-systems. First, Markov chains are used to hind-cast the observed recovery for a portfolio of buildings affected by the 2014 South Napa, California, earthquake. Next, Markov processes are used to formulate a parametric post hazard-event recovery model, which can be updated using Bayesian statistics when relevant datasets become available. Semi-Markov processes are then used to develop a more general model of single hazard recovery, which accounts for the intensity of the loading and level of damage caused by the event. Semi-Markov processes with non-renewal features are then used to account for multihazard interactions in a post-event recovery model, and applied to a case study that involves a community in Charleston, South Carolina. Lastly, Markov-type processes are combined with Bayesian networks to model the recovery of residential, commercial, educational, and industrial buildings (system-of-systems) following a hazard event. Overall, these applications demonstrate the versatility of the Markov framework towards handling recovery problems with varying levels of complexity.

42 ENGINEERING↗
DOE OSTI2017

Robust approaches to quantification of margin and uncertainty for sparse data

Characterizing the tails of probability distributions plays a key role in quantification of margins and uncertainties (QMU), where the goal is characterization of low probability, high consequence events based on continuous measures of performance. When data are collected using physical experimentation, probability distributions are typically fit using statistical methods based on the collected data, and these parametric distributional assumptions are often used to extrapolate about the extreme tail behavior of the underlying probability distribution. In this project, we character- ize the risk associated with such tail extrapolation. Specifically, we conducted a scaling study to demonstrate the large magnitude of the risk; then, we developed new methods for communicat- ing risk associated with tail extrapolation from unvalidated statistical models; lastly, we proposed a Bayesian data-integration framework to mitigate tail extrapolation risk through integrating ad- ditional information. We conclude that decision-making using QMU is a complex process that cannot be achieved using statistical analyses alone.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Multiresolution spatiotemporal mechanical model of the heart as a prior to constrain the solution for 4D models of the heart

In several nuclear cardiac imaging applications (SPECT and PET), images are formed by reconstructing tomographic data using an iterative reconstruction algorithm with corrections for physical factors involved in the imaging detection process and with corrections for cardiac and respiratory motion. The physical factors are modeled as coefficients in the matrix of a system of linear equations and include attenuation, scatter, and spatially varying geometric response. The solution to the tomographic problem involves solving the inverse of this system matrix. This requires the design of an iterative reconstruction algorithm with a statistical model that best fits the data acquisition. The most appropriate model is based on a Poisson distribution. Using Bayes Theorem, an iterative reconstruction algorithm is designed to determine the maximum a posteriori estimate of the reconstructed image with constraints that maximizes the Bayesian likelihood function for the Poisson statistical model. The a priori distribution is formulated as the joint entropy (JE) to measure the similarity between the gated cardiac PET image and the cardiac MRI cine image modeled as a FE mechanical model. In conclusion, the developed algorithm shows the potential of using a FE mechanical model of the heart derived from a cardiac MRI cine scan to constrain solutions of gated cardiac PET images.

60 APPLIED LIFE SCIENCES↗