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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Hierarchical Bayesian modeling for Inverse Uncertainty Quantification of system thermal-hydraulics code using critical flow experimental data

The best estimate plus uncertainty methodology in nuclear system thermal-hydraulic studies necessitates a comprehensive understanding of uncertainties in system code predictions. The forward uncertainty quantification (UQ) process involves the propagation of input uncertainties through the computational models to obtain uncertainties in the outputs. To this end, achieving an accurate estimation of input uncertainties is important, which is the focus of inverse UQ (IUQ). Traditionally, research in Bayesian IUQ within the nuclear engineering domain has largely relied on single-level Bayesian inference. While being effective for relatively small datasets, this approach encounters limitations for cases with large datasets. The use of a single-level model may prove inefficient, as the resultant posterior distributions can significantly differ when distinct subsets of data are employed. To address this issue, we employ an hierarchical Bayesian model for IUQ. Furthermore, this approach involves organizing observations into different groups based on the test conditions, thereby accommodating varying calibration parameters across these distinct groups. In this study, we developed and implemented a hierarchical Bayesian IUQ method to consider the grouping effect of critical flow measurement data from various geometries. Comparing the outcomes of IUQ under different selections of test data using hierarchical Bayesian IUQ against those obtained from single-level Bayesian IUQ, the forward propagation of hierarchical Bayesian IUQ results demonstrates a notably improved agreement with the experimental data.

42 ENGINEERING↗
DOE OSTI2017

Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model

Groundwater model structural error is ubiquitous, due to simplification and/or misrepresentation of real aquifer systems. During model calibration, the basic hydrogeological parameters may be adjusted to compensate for structural error. This may result in biased predictions when such calibrated models are used to forecast aquifer responses to new forcing. Here, we investigate the impact of model structural error on calibration and prediction of a real-world groundwater flow model, using a Bayesian method with a data-driven error model to explicitly account for model structural error. The error-explicit Bayesian method jointly infers model parameters and structural error and thereby reduces parameter compensation. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models (based on machine learning techniques) as a substitute for the computationally expensive groundwater model. We demonstrate that with explicit treatment of model structural error, the Bayesian method yields parameter posterior distributions that are substantially different from those derived using classical Bayesian calibration that does not account for model structural error. We also found that the error-explicit Bayesian method gives signficantly more accurate prediction along with reasonable credible intervals. Finally, through variance decomposition, we provide a comprehensive assessment of prediction uncertainty contributed from parameter, model structure, and measurement uncertainty. The results suggest that the error-explicit Bayesian approach provides a solution to real-world modeling applications for which data support the presence of model structural error, yet model deficiency cannot be specifically identified or corrected.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

A Graphical Approach to Diagnosing the Validity of the Conditional Independence Assumptions of a Bayesian Network Given Data

Bayesian networks have attained widespread use in data analysis and decision making. Well studied topics include: efficient inference, evidence propagation, parameter learning from data for complete and incomplete data scenarios, expert elicitation for calibrating Bayesian network probabilities, and structure learning. It is not uncommon for the researcher to assume the structure of the Bayesian network or to glean the structure from expert elicitation or domain knowledge. In this scenario, the model may be calibrated through learning the parameters from relevant data. There is a lack of work on model diagnostics for fitted Bayesian networks; this is the contribution of this paper. We key on the definition of (conditional) independence to develop a graphical diagnostic method which indicates if the conditional independence assumptions imposed when one assumes the structure of the Bayesian network are supported by the data. We develop the approach theoretically and describe a Monte Carlo method to generate uncertainty measures for the consistency of the data with conditional independence assumptions under the model structure. We describe how this theoretical information and the data are presented in a graphical diagnostic tool. We demonstrate the approach through data simulated from Bayesian networks under different conditional independence assumptions. We also apply the diagnostic to a real world data set. The results indicate that our approach is a reasonable way of visualizing and inspecting the conditional independence assumption of a Bayesian network given data.

Bayesian Networks · Structural Model Diagnostics ·↗
DOE OSTI2025

Bayesian event categorization matrix approach for explosion monitoring

Current efforts to correctly categorize natural events from suspected explosion sources with data that is collected by ground- or space-based sensors presents historical challenges that remain unaddressed by the Event Categorization Matrix (ECM) model. Smaller historical events (lower yield explosions) may have data available from fewer measurement techniques than are available today, and therefore, a historical event record can lack a complete set of discriminants. The covariance structures can also differ between such observations of event (source-type) categories. Both obstacles are problematic for the classic ECM model. Our work addresses this gap and presents a Bayesian update to the previous ECM model, termed the Bayesian Event Categorization Matrix model, which can be trained on partial observations and does not rely on a pooled covariance structure. We further augment the ECM model with Bayesian Decision Theory so that false negative or false positive rates of an event categorization can be reduced in an intuitive manner. To demonstrate improved categorization rates for the Bayesian Event Categorization Matrix model, we compare an array of Bayesian and classic models with multiple performance metrics using Monte Carlo experiments. We use both synthetic and real data. Our Bayesian models show consistent gains in overall accuracy and lower false negative rates relative to the classic ECM model. Here, we propose future avenues to improve Bayesian Event Categorization Matrix models’ decision making and predictive capability.

58 GEOSCIENCES↗
DOE OSTI2026

Predicting Li-Ion Battery Capacity Fade Using Early-Life Data and a Hybrid Data-Driven Gaussian Process-Bayesian Regression Approach

Accurately predicting Li-ion battery capacity trajectories using early-life data can dramatically improve battery-life understandings and be used to rapidly evaluate design/cost/performance trade-offs when developing new battery materials. Accurate early-life predictions enable researchers to quickly iterate over cell designs and material precursor properties without consistently cycling cells to failure. To this end, we present a toolbox that uses a combined Gaussian Process and Bayesian regression approach that capitalizes on signals other than just capacity (e.g., dQ/dV, voltage drops) to rapidly predict capacity-fade trajectories. The prediction tool uses Bayesian regression to fit functional forms, e.g., power law, sigmoids, etc., to predict capacity-fade dynamics. By fitting functional forms, the capacity fade can be interrogated at any point in the future, allowing for early cell-failure prediction. Additionally, Bayesian regression allows for accurate uncertainty estimates that account for cell-to-cell variability (aleatoric uncertainty) and the lack of observation data (epistemic uncertainty). By only using early cycle data to predict the capacity fade trajectory, uncertainty bounds at end-of-life can be extremely large. The large uncertainty bounds are further exacerbated because there is no systematic way to define the prior distribution of the functional forms' parameters. We improve our the predicted trajectory confidence interval of our predicted trajectory using two methods. First, we shows that a small amount of held-out cycling data is sufficientuse some train cells, that have been cycled to failure to derive information regarding the appropriate prior distributions for the functional forms' parameters of the functional form, effectively leading to data-driven priors.. We propose constructing the data-driven priors by first running a Bayesian regression starting with uninformed priors to generate intermediate cell-specific posterior parameter distributions. These posterior distributions are combined using a Ggaussian mixture model for each parameter to create the data-driven priors. These mixture models serve as the data-driven prior distributions for the parameters for. Second, we derive multiple features, e.g., C_dchg 0.5 DoD 0.5, log (|mean(dQ/dV_(w_3-w_0 ) (V)|), etc., from the train cellsheld-out cycling data, identify which the features are that best predicting capacity at early/mid-life cycles, and then create Ggaussian process regression models that are used for predicting capacity at early/mid-life cycles for the test cells (see blue dots with error bars in Fig 1b). Finally, these predicted data-points are used in addition to the actual early cycle data capacity fade to construct the Bayesian regression trajectory for the test cell s. Notably. We note that these two methods are complementary and can be combined with each other. We evaluate the performance of our proposed method on an testing open-source dataset from Iowa State University and Iowa Lakes Community College (ISU-ILCC). This dataset comprises of 251 nickel-manganese-cobalt/graphite Lithium-ion cells that are cycled under 63 different conditions. We compute the mean average percentage error (MAPE) and negative log predictive density (NLPD) to quantify the efficacy of our method. Our initial findings suggest that, when only few observations are available, for test cells, when using only Bayesian regression with uninformed priors, a power law functional provides the most accurate predictions. with very few data points. However, asHowever, a the number of data points increases, a twin sigmoidal function becomes more accurate as the number of observations further increases. We also find that using as little as 10% of the data set towards generating data-driven priors can lead to significant improvement in prediction accuracy when using early cycle data. Lastly, we found that augmenting early-cycle data with Gaussian process-predicted capacity data for Bayesian regression greatly improves the prediction accuracy. We will present a comprehensive comparison of our methods to other methods available in the literature and apply this method to additional battery datasets.

42 ENGINEERING↗
DOE OSTI2015

Principles of Bayesian Ensemble Creation: Theoretical and Empirical Observations

Bayesian methods are theoretically optimal given their underlying assumptions. Bayesian model averaging (BMA) is generally considered the standard model for creating ensembles of learners using Bayesian methods, but this technique is often out-performed by more ad hoc methods in empirical studies. It has been proposed that Bayesian model averaging struggles in practice because it accounts for uncertainty about which model is the data-generating model but still operates under the assumption that only one of them is. Thus, BMA is unable to enrich the hypothesis space as effectively as other ensemble creation methods, serving as a form of optimal model selection, not optimal model combination. This work provides empirical verification for this hypothesis using both synthetic and real-world data. We propose several different approaches for Bayesian model combination, and demonstrate that they overcome this problem with BMA. We empirically show that even the most simplistic of Bayesian model combination strategies can compete with the traditional ad hoc techniques of bagging, boosting and stacking, as well as significantly outperforming BMA over a wide variety of cases. We also explore the implications of this observation as it relates to the effectiveness of ensemble learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Order priors for Bayesian network discovery with an application to malware phylogeny

Here, Bayesian networks have been used extensively to model and discover dependency relationships among sets of random variables. We learn Bayesian network structure with a combination of human knowledge about the partial ordering of variables and statistical inference of conditional dependencies from observed data. Our approach leverages complementary information from human knowledge and inference from observed data to produce networks that reflect human beliefs about the system as well as to fit the observed data. Applying prior beliefs about partial orderings of variables is an approach distinctly different from existing methods that incorporate prior beliefs about direct dependencies (or edges) in a Bayesian network. We provide an efficient implementation of the partial-order prior in a Bayesian structure discovery learning algorithm, as well as an edge prior, showing that both priors meet the local modularity requirement necessary for an efficient Bayesian discovery algorithm. In benchmark studies, the partial-order prior improves the accuracy of Bayesian network structure learning as well as the edge prior, even though order priors are more general. Our primary motivation is in characterizing the evolution of families of malware to aid cyber security analysts. For the problem of malware phylogeny discovery, we find that our algorithm, compared to existing malware phylogeny algorithms, more accurately discovers true dependencies that are missed by other algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The utility of Bayesian data reconciliation for separations

Data reconciliation methods for separation processes typically rely on classical statistical approaches to generate estimates of true mass flow rates from measurements. Knowledge regarding the uncertainty of these estimates has value in decision making, but is often not acquired. Bayesian approaches intrinsically quantify uncertainty; however, literature for Bayesian data reconciliation of separation processes is scarce. This publication outlines two Bayesian data reconciliation models and provides details for how the models were implemented for the BayesMassBal (V 1.0.0) software package written in R. To demonstrate the advantages of this approach for data reconciliation, the models were first applied to simulated data and then compared to a classical model through a Monte Carlo experiment. In this example, the Bayesian models were found to provide more accurate estimates of the simulated data, while also providing quantitative information on the estimate uncertainty. To demonstrate the use of the technique in a practical problem, the models were also applied to real data collected from a pilot-scale rare earth solvent extraction process. Here, this publication provides a small window into how Bayesian methods can be used for data reconciliation, but findings suggest Bayesian data reconciliation models for separation processes have distinct advantages over classical alternatives.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2019

Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions

Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence intervals. Although there are statistical arguments to prefer the Bayesian approach, no direct comparison is available. In this work, we compare, directly and systematically, the frequentist and Bayesian approaches to quantifying uncertainties in direct nuclear reactions. Starting from identical initial assumptions, we determine confidence intervals associated with the elastic and the transfer process for both methods, which are evaluated against data via a comparison of the empirical coverage probabilities. Expectedly, the frequentist approach is not as flexible as the Bayesian approach in exploring parameter space and often ends up in a different minimum. We also show that the two methods produce significantly different correlations. In the end, the frequentist approach produces significantly narrower uncertainties on the considered observables than the Bayesian. Lastly, our study demonstrates that the uncertainties on the reaction observables considered here within the Bayesian approach represent reality more accurately than the much narrower uncertainties obtained using the standard frequentist approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Evaluating the Benefits of Bayesian Hierarchical Methods for Analyzing Heterogeneous Environmental Datasets: A Case Study of Marine Organic Carbon Fluxes

Large compilations of heterogeneous environmental observations are increasingly available as public databases, allowing researchers to test hypotheses across datasets. Statistical complexities arise when analyzing compiled data due to unbalanced spatial sampling, variable environmental context, mixed measurement techniques, and other reasons. Hierarchical Bayesian modeling is increasingly used in environmental science to describe these complexities, however few studies explicitly compare the utility of hierarchical Bayesian models to simpler and more commonly applied methods. Here we demonstrate the utility of the hierarchical Bayesian approach with application to a large compiled environmental dataset consisting of 5,741 marine vertical organic carbon flux observations from 407 sampling locations spanning eight biomes across the global ocean. We fit a global scale Bayesian hierarchical model that describes the vertical profile of organic carbon flux with depth. Profile parameters within a particular biome are assumed to share a common deviation from the global mean profile. Individual station-level parameters are then modeled as deviations from the common biome-level profile. The hierarchical approach is shown to have several benefits over simpler and more common data aggregation methods. First, the hierarchical approach avoids statistical complexities introduced due to unbalanced sampling and allows for flexible incorporation of spatial heterogeneitites in model parameters. Second, the hierarchical approach uses the whole dataset simultaneously to fit the model parameters which shares information across datasets and reduces the uncertainty up to 95% in individual profiles. Third, the Bayesian approach incorporates prior scientific information about model parameters; for example, the non-negativity of chemical concentrations or mass-balance, which we apply here. We explicitly quantify each of these properties in turn. We emphasize the generality of the hierarchical Bayesian approach for diverse environmental applications and its increasing feasibility for large datasets due to recent developments in Markov Chain Monte Carlo algorithms and easy-to-use high-level software implementations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

An analysis of Bayesian estimates for missing higher orders in perturbative calculations

With current high precision collider data, the reliable estimation of theoretical uncertainties due to missing higher orders (MHOs) in perturbation theory has become a pressing issue for collider phenomenology. Traditionally, the size of the MHOs is estimated through scale variation, a simple but ad hoc method without probabilistic interpretation. Bayesian approaches provide a compelling alternative to estimate the size of the MHOs, but it is not clear how to interpret the perturbative scales, like the factorisation and renormalisation scales, in a Bayesian framework. Recently, it was proposed that the scales can be incorporated as hidden parameters into a Bayesian model. In this paper, we thoroughly scrutinise Bayesian approaches to MHO estimation and systematically study the performance of different models on an extensive set of high-order calculations. We extend the framework in two significant ways. First, we define a new model that allows for asymmetric probability distributions. Second, we introduce a prescription to incorporate information on perturbative scales without interpreting them as hidden model parameters. We clarify how the two scale prescriptions bias the result towards specific scale choice, and we discuss and compare different Bayesian MHO estimates among themselves and to the traditional scale variation approach. Finally, we provide a practical prescription of how existing perturbative results at the standard scale variation points can be converted to 68%/95% credibility intervals in the Bayesian approach using the new public code MiHO.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Applications of emulation and Bayesian methods in heavy-ion physics

Abstract Heavy-ion collisions provide a window into the properties of many-body systems of deconfined quarks and gluons. Understanding the collective properties of quarks and gluons is possible by comparing models of heavy-ion collisions to measurements of the distribution of particles produced at the end of the collisions. These model-to-data comparisons are extremely challenging, however, because of the complexity of the models, the large amount of experimental data, and their uncertainties. Bayesian inference provides a rigorous statistical framework to constrain the properties of nuclear matter by systematically comparing models and measurements. This review covers model emulation and Bayesian methods as applied to model-to-data comparisons in heavy-ion collisions. Replacing the model outputs (observables) with Gaussian process emulators is key to the Bayesian approach currently used in the field, and both current uses of emulators and related recent developments are reviewed. The general principles of Bayesian inference are then discussed along with other Bayesian methods, followed by a systematic comparison of seven recent Bayesian analyses that studied quark-gluon plasma properties, such as the shear and bulk viscosities. The latter comparison is used to illustrate sources of differences in analyses, and what it can teach us for future studies.

Paquet, Jean-François (ORCID:0000000187368171)↗
DOE OSTI2019

An Efficient Bayesian Method for Advancing the Application of Deep Learning in Earth Science

Despite their wide and successful applications, deep learning (DL) models are prone to overfitting for small training datasets, produce a poor predictive performance for uncertain data, and provide point estimations without any indication of the accuracy and credibility. These limitations of the deterministic DL models hinder their effective application in Earth system science where the labelled data are sparse, noisy and incomplete with large uncertainty and where the predictive uncertainty quantification is needed for scientific understanding and policy decision making. Integration of Bayesian inference into DL models adds an estimate of uncertainty and regularization in the predictions. However, traditional Bayesian methods are computationally unaffordable and inflexible for high-dimensional problems, which limits their application to DL systems that typically have millions of model parameters. In this effort, we propose an efficient and general-purpose Bayesian inference method to advance DL model optimization and uncertainty quantification, so as to facilitate the adoption of DL in Earth sciences. In a demonstration, we integrate the proposed Bayesian method with a feedforward neural network (NN) to build a fast-to-evaluate surrogate of the complex Energy Exascale Earth System Land Model for efficient modeling. The formulated Bayesian NN, using a small number of training data, produces an accurate prediction with high credibility, whereas with the same small training size, the deterministic NN cannot yield a reasonable estimation and does not provide confidence information. The proposed Bayesian method is computationally efficient and flexible, capable of integration with diverse network variants such as convolutional NNs and recurrent NNs to advance the application of DL in Earth sciences.

Lu, Dan↗
DOE OSTI2013

A support vector machine classifier reduces interscanner variation in the HRCT classification of regional disease pattern in diffuse lung disease: Comparison to a Bayesian classifier

Purpose: To investigate the effect of using different computed tomography (CT) scanners on the accuracy of high-resolution CT (HRCT) images in classifying regional disease patterns in patients with diffuse lung disease, support vector machine (SVM) and Bayesian classifiers were applied to multicenter data. Methods: Two experienced radiologists marked sets of 600 rectangular 20 Multiplication-Sign 20 pixel regions of interest (ROIs) on HRCT images obtained from two scanners (GE and Siemens), including 100 ROIs for each of local patterns of lungs-normal lung and five of regional pulmonary disease patterns (ground-glass opacity, reticular opacity, honeycombing, emphysema, and consolidation). Each ROI was assessed using 22 quantitative features belonging to one of the following descriptors: histogram, gradient, run-length, gray level co-occurrence matrix, low-attenuation area cluster, and top-hat transform. For automatic classification, a Bayesian classifier and a SVM classifier were compared under three different conditions. First, classification accuracies were estimated using data from each scanner. Next, data from the GE and Siemens scanners were used for training and testing, respectively, and vice versa. Finally, all ROI data were integrated regardless of the scanner type and were then trained and tested together. All experiments were performed based on forward feature selection and fivefold cross-validation with 20 repetitions. Results: For each scanner, better classification accuracies were achieved with the SVM classifier than the Bayesian classifier (92% and 82%, respectively, for the GE scanner; and 92% and 86%, respectively, for the Siemens scanner). The classification accuracies were 82%/72% for training with GE data and testing with Siemens data, and 79%/72% for the reverse. The use of training and test data obtained from the HRCT images of different scanners lowered the classification accuracy compared to the use of HRCT images from the same scanner. For integrated ROI data obtained from both scanners, the classification accuracies with the SVM and Bayesian classifiers were 92% and 77%, respectively. The selected features resulting from the classification process differed by scanner, with more features included for the classification of the integrated HRCT data than for the classification of the HRCT data from each scanner. For the integrated data, consisting of HRCT images of both scanners, the classification accuracy based on the SVM was statistically similar to the accuracy of the data obtained from each scanner. However, the classification accuracy of the integrated data using the Bayesian classifier was significantly lower than the classification accuracy of the ROI data of each scanner. Conclusions: The use of an integrated dataset along with a SVM classifier rather than a Bayesian classifier has benefits in terms of the classification accuracy of HRCT images acquired with more than one scanner. This finding is of relevance in studies involving large number of images, as is the case in a multicenter trial with different scanners.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Improvement and generalization of ABCD method with Bayesian inference

To find New Physics or to refine our knowledge of the Standard Model at the LHC is an enterprise that involves many factors, such as the capabilities and the performance of the accelerator and detectors, the use and exploitation of the available information, the design of search strategies and observables, as well as the proposal of new models. We focus on the use of the information and pour our effort in re-thinking the usual data-driven ABCD method to improve it and to generalize it using Bayesian Machine Learning techniques and tools. We propose that a dataset consisting of a signal and many backgrounds is well described through a mixture model. Signal, backgrounds and their relative fractions in the sample can be well extracted by exploiting the prior knowledge and the dependence between the different observables at the event-by-event level with Bayesian tools. We show how, in contrast to the ABCD method, one can take advantage of understanding some properties of the different backgrounds and of having more than two independent observables to measure in each event. In addition, instead of regions defined through hard cuts, the Bayesian framework uses the information of continuous distribution to obtain soft-assignments of the events which are statistically more robust. To compare both methods we use a toy problem inspired by pp\to hh\to b\bar b b \bar b p p → h h → b b ‾ b b ‾ , selecting a reduced and simplified number of processes and analysing the flavor of the four jets and the invariant mass of the jet-pairs, modeled with simplified distributions. Taking advantage of all this information, and starting from a combination of biased and agnostic priors, leads us to a very good posterior once we use the Bayesian framework to exploit the data and the mutual information of the observables at the event-by-event level. We show how, in this simplified model, the Bayesian framework outperforms the ABCD method sensitivity in obtaining the signal fraction in scenarios with 1% and 0.5% true signal fractions in the dataset. We also show that the method is robust against the absence of signal. We discuss potential prospects for taking this Bayesian data-driven paradigm into more realistic scenarios.

Alvarez, Ezequiel↗