Search NASA⌕ Search

SEARCH · Search NASA

Results for “Variational Bayesian”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation. We assume a parameterized Gaussian prior on the unknown functions, and approximate the posterior density by a parameterized multivariate Gaussian density. The parameters of the prior and posterior are estimated from sparse observations of the PDE model's states and the unknown functions themselves by maximizing the evidence lower bound (ELBO), a lower bound on the log marginal likelihood of the observations. The first method, Laplace-EM, employs the expectation maximization algorithm to maximize the ELBO, with a Laplace approximation of the posterior on the E-step, and minimization of a Kullback-Leibler divergence on the M-step. The second method, DSVI-EB, employs the doubly stochastic variational inference (DSVI) algorithm, in which the ELBO is maximized via gradient-based stochastic optimization, with nosiy gradients computed via simple Monte Carlo sampling and Gaussian backpropagation. We apply these methods to identifying diffusion coefficients in linear and nonlinear diffusion equations, and we find that both methods provide accurate estimates of posterior densities and the hyperparameters of Gaussian priors. While the Laplace-EM method is more accurate, it requires computing Hessians of the physics model. The DSVI-EB method is found to be less accurate but only requires gradients of the physics model.

approximate Bayesian inference, model inversion, v↗
DOE OSTI2020

Dependence of the impurity transport on the dominant turbulent regime in ELM-y H-mode discharges on the DIII-D tokamak

Laser blow-off injections of aluminum and tungsten have been performed on the DIII-D tokamak to investigate the variation of impurity transport in a set of dedicated ion and electron heating scans with a fixed value of the external torque. The particle transport is quantified via the Bayesian inference method, which, constrained by a combination of a charge exchange recombination spectroscopy, soft X-ray measurements, and VUV spectroscopy provides a detailed uncertainty quantification of transport coefficients. Contrasting discharge phases with a dominant electron and ion heating reveal 3-fold drop in the impurity confinement time and order of magnitude increase in midradius impurity diffusion, when additional electron heating is applied. Further, the calculated stationary aluminum density profiles reverse from peaked in electron heated to hollow in the ion heated case, following a similar trend as electron and carbon density. Comparable values of a core diffusion have been observed for W and Al ions, while differences in the propagation dynamics of these impurities are attributed to pedestal and edge transport. Modeling of the core transport with non-linear gyrokinetics code CGYRO, significantly underpredicts the magnitude of the variation in Al transport. Diffusion increases 3-times steeper with additional electron heat flux and 10-times lower diffusion is observed in ion heated case than predicted by the modeling. Here, the CGYRO model quantitatively matches the increase of the Al diffusion when approaching the linear threshold for the transition from the ion temperature gradient (ITG) to trapped electron mode (TEM).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

MODEL COMPARISON FOR THE DENSITY STRUCTURE ACROSS SOLAR CORONAL WAVEGUIDES

The spatial variation of physical quantities, such as the mass density, across solar atmospheric waveguides governs the timescales and spatial scales for wave damping and energy dissipation. The direct measurement of the spatial distribution of density, however, is difficult, and indirect seismology inversion methods have been suggested as an alternative. We applied Bayesian inference, model comparison, and model-averaging techniques to the inference of the cross-field density structuring in solar magnetic waveguides using information on periods and damping times for resonantly damped magnetohydrodynamic transverse kink oscillations. Three commonly employed alternative profiles were used to model the variation of the mass density across the waveguide boundary. Parameter inference enabled us to obtain information on physical quantities such as the Alfvén travel time, the density contrast, and the transverse inhomogeneity length scale. The inference results from alternative density models were compared and their differences quantified. Then, the relative plausibility of the considered models was assessed by performing model comparison. Our results indicate that the evidence in favor of any of the three models is minimal, unless the oscillations are strongly damped. In such a circumstance, the application of model-averaging techniques enables the computation of an evidence-weighted inference that takes into account the plausibility of each model in the calculation of a combined inversion for the unknown physical parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A Graphical Model for Fusing Diverse Microbiome Data

This paper develops a Bayesian graphical model for fusing disparate types of count data. The motivating application is the study of bacterial communities from diverse high-dimensional features, in this case, transcripts, collected from different treatments. In such datasets, there are no explicit correspondences between the communities and each corresponds to different factors, making data fusion challenging. We introduce a flexible multinomial-Gaussian generative model for jointly modeling such count data. This latent variable model jointly characterizes the observed data through a common multivariate Gaussian latent space that parameterizes the set of multinomial probabilities of the transcriptome counts. The covariance matrix of the latent variables induces a covariance matrix of co-dependencies between all the transcripts, effectively fusing multiple data sources. We present a computationally scalable variational Expectation-Maximization (EM) algorithm for inferring the latent variables and the parameters of the model. Here, the inferred latent variables provide a common dimensionality reduction for visualizing the data and the inferred parameters provide a predictive posterior distribution. In addition to simulation studies that demonstrate the variational EM procedure, we apply our model to a bacterial microbiome dataset.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Calibration and uncertainty quantification for Davis Equation of State models for the High Explosive PBX 9501 products

Abstract This paper investigates the uncertainty in the parameters used in the calibration of an Davis Equation Of State (EOS) for the detonation products of the High Explosive PBX 9501. The procedure sought to make use of all available information about this HE to inform the best set of calibration parameters as well as the uncertainty in these parameters. The procedure made use of historical experimental data, the results from thermo‐chemical modeling as well as data on the best isentrope function fit to cylinder test experimental data. Combining all these heterogeneous data sources together in a Bayesian calibration, yielded a posterior mean and covariance. Sampling from the posterior distribution and evaluating an important Quantity Of Interest (QOI) in the EOS model, the detonation speed of a one‐inch rate stick, produced a distribution which showed variations which were in agreement with experiments. The uncertainty in the EOS was reported as eleven sets of model calibrations which spanned the range of this QOI.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2017

Modeling Soot Oxidation and Gasification with Bayesian Statistics

This paper presents a statistical method for model calibration using data collected from literature. The method is used to calibrate parameters for global models of soot consumption in combustion systems. This consumption is broken into two different submodels: first for oxidation where soot particles are attacked by certain oxidizing agents; second for gasification where soot particles are attacked by H 2 O or CO 2 molecules. Rate data were collected from 19 studies in the literature and evaluated using Bayesian statistics to calibrate the model parameters. Bayesian statistics are valued in their ability to quantify uncertainty in modeling. The calibrated consumption model with quantified uncertainty is presented here along with a discussion of associated implications. The oxidation results are found to be consistent with previous studies. Significant variation is found in the CO 2 gasification rates.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2026

Accessing the gluon momentum fraction of nucleons through the gradient flow

We calculate the gluon momentum fraction of the nucleon using lattice QCD, with a nonperturbative renormalization technique based on the gradient flow. The gluon momentum fraction is determined on a single Wilson-clover ensemble using 𝑁 𝑓 =2 +1 flavors with pion mass 358 MeV and lattice spacing 0.094 fm. We employ the variational method to reduce excited-state contamination and apply the distillation framework to ensure a large operator basis. To reduce systematic uncertainties, we apply Bayesian model averaging to all fit procedures. We apply matching coefficients to the flow-time dependent lattice results to recover the gluon momentum fraction in the $\overline{MS}$-scheme at 2 GeV. Our final result is ⟨𝑥⟩ 𝑔 ⁢(𝜇 =2 GeV) =0.482⁢(35), where we quote only statistical uncertainties.

Lattice QCD↗
DOE OSTI2017

Quantification of uncertainty in photon source spot size inference during laser-driven radiography experiments at TRIDENT

Images of the R2DTO resolution target were obtained during laser-driven-radiography experiments performed at the TRIDENT laser facility, and analysis of these images using the Bayesian Inference Engine (BIE) determines a most probable full-width half maximum (FWHM) spot size of 78 μm. However, significant uncertainty prevails due to variation in the measured detector blur. Propagating this uncertainty in detector blur through the forward model results in an interval of probabilistic ambiguity spanning approximately 35-195 μm when the laser energy impinges on a thick (1 mm) tantalum target. In other phases of the experiment, laser energy is deposited on a thin (~100 nm) aluminum target placed 250 μm ahead of the tantalum converter. When the energetic electron beam is generated in this manner, upstream from the bremsstrahlung converter, the inferred spot size shifts to a range of much larger values, approximately 270-600 μm FWHM. This report discusses methods applied to obtain these intervals as well as concepts necessary for interpreting the result within a context of probabilistic quantitative inference.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities

Here we propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ~ 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.

42 ENGINEERING↗
DOE OSTI2018

Robust Bayesian Calibration of a k-ε Model for Compressible Jet-in-Crossflow Simulations

Compressible jet-in-crossflow interactions are difficult to simulate accurately using Reynolds-averaged Navier–Stokes (RANS) models. This could be due to simplifications inherent in RANS or the use of inappropriate RANS constants estimated by fitting to experiments of simple or canonical flows. Our previous work on Bayesian calibration of a k-ε model to experimental data had led to a weak hypothesis that inaccurate simulations could be due to inappropriate constants more than model-form inadequacies of RANS. In this work, Bayesian calibration of k-ε constants to a set of experiments that span a range of Mach numbers and jet strengths has been performed. The variation of the calibrated constants has been checked to assess the degree to which parametric estimates compensate for RANS’s model-form errors. An analytical model of jet-in-crossflow interactions has also been developed, and estimates of k-ε constants that are free of any conflation of parametric and RANS’s model-form uncertainties have been obtained. It has been found that the analytical k-ε constants provide mean-flow predictions that are similar to those provided by the calibrated constants. Further, both of them provide predictions that are far closer to experimental measurements than those computed using “nominal” values of these constants simply obtained from the literature. It can be concluded that the lack of predictive skill of RANS jet-in-crossflow simulations is mostly due to parametric inadequacies, and our analytical estimates may provide a simple way of obtaining predictive compressible jet-in-crossflow simulations.

42 ENGINEERING↗
DOE OSTI2016

ALMA-SZ detection of a galaxy cluster merger shock at half the age of the universe

We present ALMA measurements of a merger shock using the thermal Sunyaev–Zel’dovich (SZ) effect signal, at the location of a radio relic in the famous El Gordo galaxy cluster at z≈0.9. Multi-wavelength analysis in combination with the archival Chandra data and a high-resolution radio image provides a consistent picture of the thermal and non-thermal signal variation across the shock front and helps to put robust constraints on the shock Mach number as well as the relic magnetic field. We employ a Bayesian analysis technique for modeling the SZ and X-ray data self-consistently, illustrating respective parameter degeneracies. Combined results indicate a shock with Mach number M=2.4{sub −0.6}{sup +1.3}, which in turn suggests a high value of the magnetic field (of the order of 4–10 μG) to account for the observed relic width at 2 GHz. At roughly half the current age of the universe, this is the highest-redshift direct detection of a cluster shock to date, and one of the first instances of an ALMA-SZ observation in a galaxy cluster. It shows the tremendous potential for future ALMA-SZ observations to detect merger shocks and other cluster substructures out to the highest redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

MFNets: Multifidelity data-driven networks for Bayesian learning and prediction

This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Learning occupants’ indoor comfort temperature through a Bayesian inference approach for office buildings in United States

A carefully chosen indoor comfort temperature as the thermostat set-point is the key to optimizing building energy use and occupants’ comfort and well-being. ASHRAE Standard 55 or ISO Standard 7730 uses the PMV-PPD model or the adaptive comfort model that is based on small-sized or outdated sample data, which raises questions on whether and how ranges of occupant thermal comfort temperature should be revised using more recent larger-sized dataset. In this paper, a Bayesian inference approach has been used to derive new occupant comfort temperature ranges for U.S. office buildings using the ASHRAE Global Thermal Comfort Database. Bayesian inference can express uncertainty and incorporate prior knowledge. The comfort temperatures were found to be higher and less variable at cooling mode than at heating mode, and with significant overlapped variation ranges between the two modes. The comfort operative temperature of occupants varies between 21.9 and 25.4 °C for the cooling mode with a median of 23.7 °C, and between 20.5 and 24.9 °C for the heating mode with a median of 22.7 °C. These comfort temperature ranges are similar to the current ASHRAE standard 55 in the heating mode but 2–3 °C lower in the cooling mode. Finally, the results of this study could be adopted as more realistic thermostat set-points in building design, operation, control optimization, energy performance analysis, and policymaking.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2015

A Bayesian Meta-Analysis of the Effect of Alcohol Use on HCV-Treatment Outcomes with a Comparison of Resampling Methods to Assess Uncertainty in Parameter Estimates.

There is mounting evidence that alcohol use is significantly linked to lower HCV treatment response rates in interferon-based therapies, though some of the evidence is conflicting. Furthermore, although health care providers recommend reducing or abstaining from alcohol use prior to treatment, many patients do not succeed in doing so. The goal of this meta-analysis was to systematically review and summarize the Englishlanguage literature up through January 30, 2015 regarding the relationship between alcohol use and HCV treatment outcomes, among patients who were not required to abstain from alcohol use in order to receive treatment. Seven pertinent articles studying 1,751 HCV-infected patients were identified. Log-ORs of HCV treatment response for heavy alcohol use and light alcohol use were calculated and compared. We employed a hierarchical Bayesian meta-analytic model to accommodate the small sample size. The summary estimate for the log-OR of HCV treatment response was -0.775 with a 95% credible interval of (-1.397, -0.236). The results of the Bayesian meta-analysis are slightly more conservative compared to those obtained from a boot-strapped, random effects model. We found evidence of heterogeneity (Q = 14.489, p = 0.025), accounting for 60.28% of the variation among log-ORs. Meta-regression to capture the sources of this heterogeneity did not identify any of the covariates investigated as significant. This meta-analysis confirms that heavy alcohol use is associated with decreased HCV treatment response compared to lighter levels of alcohol use. Further research is required to characterize the mechanism by which alcohol use affects HCV treatment response.

alcohol↗
DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗
DOE OSTI2019

Model-Based Localizatiion in a Shallow Ocean Environment: A Sequential Bayesian/Optimization Approach

The shallow ocean is a dynamically changing medium leading to nonstationary statistical behavior when subjected to temperature, wind, surface variations, bottom interactions, noise and extraneous disturbances as well as other conditions that render it a uniquely challenging environment — especially from a signal processing perspective. Processors must account for and adapt to such instantaneous changes in order to be effective. Thus, a processor is required to “adapt” to these environmental variations while simultaneously providing meaningful estimates that are necessary for such applications as detection, localization, inversion and enhancement. In this paper, we develop a parametrically adaptive, sequential Bayesian processor capable of jointly estimating both modal functions and environmental parameters to provide enhanced estimates for a focused optimizer capable locating a target in the noisy shallow ocean environment.

42 ENGINEERING↗