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DOE OSTI2025

Hierarchical Bayesian Modeling for Cosmology: Can NPE reliably replace MCMC?

Hierarchical neural posterior estimation has its place Hierarchical Bayesian Modeling (HBM) combined with MCMC algorithms has been shown to provide more robust and accurate inference for real-world phenomena in which nature takes a nested form. However, MCMC-based inference can be computationally expensive, and its performance often suffers for complex posterior geometries. These costs are especially pertinent for HBM. Studies have recently demonstrated the potential for a flexible, expressive, and amortized hierarchical neural posterior estimator (HNPE) built on Normalizing Flows. These studies have mostly been performed on simple datasets, or they focus on a single parameter from each level of the hierarchy. A systematic study analyzing how both hierarchical methods compare for more complex and realistic datasets is necessary before applying HNPE for scientific measurements. Here, we re-explore the theory behind HNPE and conduct comparative numerical experiments of HNPE and MCMC-based HBM methods on real and synthetic data, including strong gravitational lensing simulations. In particular, we use a suite of diagnostics to show trade-offs in terms of accuracy, precision, time to train or sample, reproducibility, and the need for expert domain knowledge. Especially for higher dimensional and complex posteriors, HNPE is expected to drastically improve on time for inference, accuracy, and precision with an upfront training time cost.

Hur, Rachel [Chicago U.] (ORCID:000900089890445X)↗

NASA NTRS2008

Potential Use of a Bayesian Network for Discriminating Flash Type from Future GOES-R Geostationary Lightning Mapper (GLM) data

Continuous monitoring of the ratio of cloud flashes to ground flashes may provide a better understanding of thunderstorm dynamics, intensification, and evolution, and it may be useful in severe weather warning. The National Lighting Detection Network TM (NLDN) senses ground flashes with exceptional detection efficiency and accuracy over most of the continental United States. A proposed Geostationary Lightning Mapper (GLM) aboard the Geostationary Operational Environmental Satellite (GOES-R) will look at the western hemisphere, and among the lightning data products to be made available will be the fundamental optical flash parameters for both cloud and ground flashes: radiance, area, duration, number of optical groups, and number of optical events. Previous studies have demonstrated that the optical flash parameter statistics of ground and cloud lightning, which are observable from space, are significantly different. This study investigates a Bayesian network methodology for discriminating lightning flash type (ground or cloud) using the lightning optical data and ancillary GOES-R data. A Directed Acyclic Graph (DAG) is set up with lightning as a "root" and data observed by GLM as the "leaves." This allows for a direct calculation of the joint probability distribution function for the lighting type and radiance, area, etc. Initially, the conditional probabilities that will be required can be estimated from the Lightning Imaging Sensor (LIS) and the Optical Transient Detector (OTD) together with NLDN data. Directly manipulating the joint distribution will yield the conditional probability that a lightning flash is a ground flash given the evidence, which consists of the observed lightning optical data [and possibly cloud data retrieved from the GOES-R Advanced Baseline Imager (ABI) in a more mature Bayesian network configuration]. Later, actual GLM and NLDN data can be used to refine the estimates of the conditional probabilities used in the model; i.e., the Bayesian network is a learning network. Methods for efficient calculation of the conditional probabilities (e.g., an algorithm using junction trees), finding data conflicts, goodness of fit, and dealing with missing data will also be addressed.

Solakiewiz, Richard↗

NASA NTRS2023

A Sensitive Search for Supernova Emission Associated with the Extremely Energetic and Nearby GRB 221009A

We report observations of the optical counterpart of the long gamma-ray burst GRB 221009A. Due to the extreme rarity of being both nearby (z = 0.151) and highly energetic (E ϒ,iso ≥ 10 54 erg), GRB 221009A offers a unique opportunity to probe the connection between massive star core collapse and relativistic jet formation across a very broad range of γ-ray properties. Adopting a phenomenological power-law model for the afterglow and host galaxy estimates from high-resolution Hubble Space Telescope imaging, we use Bayesian model comparison techniques to determine the likelihood of an associated supernova (SN) contributing excess flux to the optical light curve. Though not conclusive, we find moderate evidence (K Bayes =10 1.2 for the presence of an additional component arising from an associated SN, SN 2022xiw, and find that it must be substantially fainter (<67% as bright at the 99% confidence interval) than SN 1998bw. Given the large and uncertain line-of-sight extinction, we attempt to constrain the SN parameters (M Ni , M ej and E KE ) under several different assumptions with respect to the host galaxy's extinction. We find properties that are broadly consistent with previous GRB-associated SNe: M Ni = 0.05–0.25 M ⊙ , M ej = 3.5–11.1 M ⊙ , and E KE = (1.6–5.2) × 10 52 erg. We note that these properties are weakly constrained due to the faintness of the SN with respect to the afterglow and host emission, but we do find a robust upper limit on M Ni of M Ni < 0.36 M ⊙ . Given the tremendous range in isotropic gamma-ray energy release exhibited by GRBs (seven orders of magnitude), the SN emission appears to be decoupled from the central engine in these systems.

Core-collapse supernovae↗

DOE OSTI2021

Application of Sequential Design of Experiments (SDoE) to Large Pilot-Scale Solvent-Based CO2 Capture Process at Technology Centre Mongstad (TCM)

The United States Department of Energy’s Carbon Capture Simulation for Industry Impact (CCSI2) program has developed a framework for sequential design of experiments (SDoE) that aims to maximize knowledge gained from budget- and schedule-limited pilot scale testing. SDoE was applied to the planning and execution of campaigns for testing CO2 capture systems at pilot-scale in order to optimally allocate resources available for the testing. In this methodology, a stochastic process model is developed by quantifying the parametric uncertainty in submodels of interest; for a solvent-based CO2 capture system, these may include physical properties and equipment performance submodels (e.g., mass transfer, interfacial area). This uncertainty is propagated through the full process model, over variable operating conditions, for estimating the resulting uncertainty in key model outputs (e.g., percentage of CO2 capture, solvent regeneration energy requirement). In developing a data collection plan, the predicted output uncertainty is incorporated into an algorithm that seeks simultaneously to select process operating conditions for which the predicted uncertainty is relatively high and to ensure that the entire space of operation is well represented. This test plan is then used to guide operation of the pilot plant at varying steady-state conditions, with resulting process data incorporated into the existing model using Bayesian inference to refine parameter distributions. The updated stochastic model, with reduced parametric uncertainty from data collected, is then used to guide additional data collection, thus the sequential nature of the experimental design. The SDoE process was implemented at the pilot test unit (12 MWe in scale) at Norway’s Technology Centre Mongstad (TCM) in a summer 2018 test campaign with aqueous monoethanolamine (MEA). During the test campaign, the varied operating conditions included the flowrates of circulated solvent, flue gas, and reboiler steam and the CO2 concentration in the flue gas. The process data were used to update probability distributions of mass transfer and interfacial area parameters of a stochastic process model developed by the CCSI2 team. Two iterations of the SDoE process were executed, resulting in the uncertainty in model predicted CO2 capture percentage decreasing by an average of 58.0 ± 4.7% over the full input space of interest. This work demonstrates the potential of the SDoE process for model refinement through reduction in process model parametric uncertainty, and ultimately risk in scale-up, in CO2 capture technology performance.

carbon capture↗

DOE OSTI2022

Bayesian analysis of nuclear polarizability corrections to the Lamb shift of muonic H-atoms and He-ions

The extraction of nuclear charge radii from spectroscopy experiments in muonic atoms is currently limited by the large uncertainties associated with the theoretical evaluation of the nuclear polarizability effects. To facilitate calculations, these polarizability corrections are conventionally expressed as an expansion in a dimensionless parameter η, which has been argued in previous literature to hold an approximate value of 0.33 in light-nuclear systems. In this work, we check this claim by doing a Bayesian analysis of the nuclear-polarizability corrections to the Lamb shift in µ 2 H and µ 3 H atoms and in µ 3 He + and µ 4 He + ions at various orders in the η-expansion. As presented here, our analysis supports the claim that η $\ll$ 1 in these systems and finds truncation uncertainties that are similar to the previous estimate, the only exception being the truncation uncertainties in the µ 3 He + ion, which are found to be larger.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Far-field thermal imaging below diffraction limit

Non-uniform self-heating and temperature hotspots are major concerns compromising the performance and reliability of submicron electronic and optoelectronic devices. At deep submicron scales where effects such as contact-related artifacts and diffraction limits accurate measurements of temperature hotspots, non-contact thermal characterization can be extremely valuable. In this work, we use a Bayesian optimization framework with generalized Gaussian Markov random field (GGMRF) prior model to obtain accurate full-field temperature distribution of self-heated metal interconnects from their thermoreflectance thermal images (TRI) with spatial resolution 2.5 times below Rayleigh limit for 530nm illumination. Finite element simulations along with TRI experimental data were used to characterize the point spread function of the optical imaging system. In addition, unlike iterative reconstruction algorithms that use ad hoc regularization parameters in their prior models to obtain the best quality image, we used numerical experiments and finite element modeling to estimate the regularization parameter for solving a real experimental inverse problem.

42 ENGINEERING↗

DOE OSTI2022

A probabilistic inverse prediction method for predicting plutonium processing conditions

In the past decade, nuclear chemists and physicists have been conducting studies to investigate the signatures associated with the production of special nuclear material (SNM). In particular, these studies aim to determine how various processing parameters impact the physical, chemical, and morphological properties of the resulting special nuclear material. By better understanding how these properties relate to the processing parameters, scientists can better contribute to nuclear forensics investigations by quantifying their results and ultimately shortening the forensic timeline. This paper aims to statistically analyze and quantify the relationships that exist between the processing conditions used in these experiments and the various properties of the nuclear end-product by invoking inverse methods. In particular, these methods make use of Bayesian Adaptive Spline Surface models in conjunction with Bayesian model calibration techniques to probabilistically determine processing conditions as an inverse function of morphological characteristics. Not only does the model presented in this paper allow for providing point estimates of a sample of special nuclear material, but it also incorporates uncertainty into these predictions. This model proves sufficient for predicting processing conditions within a standard deviation of the observed processing conditions, on average, provides a solid foundation for future work in predicting processing conditions of particles of special nuclear material using only their observed morphological characteristics, and is generalizable to the field of chemometrics for applicability across different materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2019

How Much Testing is Needed to Manage Supportability Risks for Beyond-LEO Missions?

Supportability will be a significantly greater driver of cost and risk for future deep-space crewed missions than it has been in the past. Spares requirements and maintenance risk mitigation in particular present an unprecedented challenge for missions beyond Low Earth Orbit (LEO), since, for the first time in human spaceflight history, crews will be weeks or months away from resupply or a safe return to Earth in the event of an abort. Under these conditions, failure rates are a critical parameter that must be well-understood in order to manage logistics and risk effectively. However, failure rates cannot be measured directly, and can only be estimated based on past experience and test results. Previous research has shown that International Space Station (ISS) operational experience has provided significant benefits to future missions by reducing uncertainty and improving accuracy in failure rate estimates, resulting in significant reductions in mass and risk for beyond-LEO missions. This paper updates and expands on that research and quantifies the potential value of continued testing for future mission supportability. Frequentist and Bayesian models for evaluating, validating, and updating failure rate estimates are described, and are combined with supportability models to examine potential impacts of additional operating experience for future missions in terms of logistics mass reduction. The implications of these results for technology development, system design, and program planning are discussed along with lessons learned and recommendations for future system development. In the end, there is no simple answer to the question of how much testing is required, but the models described in this paper provide a way to evaluate the potential impacts of testing in order to inform test planning.

Andrew C Owens↗

DOE OSTI2021

Sensitivity Analysis of Particle-In-Cell Modeling Parameters in Settling Bed, Bubbling Fluidized Bed and Circulating Fluidized Bed

The objective of the work presented is to perform a preliminary sensitivity analysis of particle-in-cell (PIC) model parameters when applied to settling bed, bubbling fluidized bed, and circulating fluidized bed simulations. These examples correspond to widely different flow conditions commonly seen in chemical engineering applications. Simulations were performed using the PIC method in the open-source software Multiphase Flow with Interphase eXchanges (MFiX) developed by the National Energy Technology Laboratory (NETL). As part of the non-intrusive uncertainty quantification (UQ) analysis, simulation campaigns were generated using Nodeworks. Sampling locations or settings for PIC model parameters were determined using the Latin Hypercube method. Response surfaces were created using radial basis functions (RBF), and Sobol’ indices were estimated to quantify the influence of model parameters on the quantities of interest (QoI). This study marks a first step towards systematically determining optimal ranges for model parameters used in MFiX-PIC. Based on limited experience, it is expected that these values would depend strongly on flow conditions. Given the complexity of the multiphase flow systems under analysis, a non-intrusive UQ based approach is used to identify the most influential parameters in each case. This prior knowledge will help in proposing an effective design of experiments (DoE) and determine optimal parameters through techniques such as deterministic or Bayesian calibration, which will be pursued in the future.

42 ENGINEERING↗

DOE OSTI2021

Discrete-Direct Model Calibration and Uncertainty Propagation Method Confirmed on Multi-Parameter Plasticity Model Calibrated to Sparse Random Field Data

A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures.

42 ENGINEERING↗

NASA NTRS2019

Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics

In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.

Elrod, Chris↗

NASA NTRS2014

Reconstructing the Sky Location of Gravitational-Wave Detected Compact Binary Systems: Methodology for Testing and Comparison

The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and "triangulation-based" techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiralonly signals from compact binary systems with a total mass of equal to or less than 20M solar mass and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor approx. equals 20 smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor approx. equals 1000 longer processing time.

technique used↗

DOE OSTI2022

Feasibility of Vascular Parameter Estimation for Assessing Hypertensive Pregnancy Disorders

Abstract Hypertensive pregnancy disorders (HPDs), such as pre-eclampsia, are leading sources of both maternal and fetal morbidity in pregnancy. Noninvasive imaging, such as ultrasound (US) and magnetic resonance imaging (MRI), is an important tool for predicting and monitoring these high risk pregnancies. While imaging can measure hemodynamic parameters, such as uterine artery pulsatility and resistivity indices (PI and RI), the interpretation of such metrics for disease assessment relies on ad hoc standards, which provide limited insight to the physical mechanisms underlying the emergence of hypertensive pregnancy disorders. To provide meaningful interpretation of measured hemodynamic data in patients, advances in computational fluid dynamics can be brought to bear. In this work, we develop a patient-specific computational framework that combines Bayesian inference with a reduced-order fluid dynamics model to infer parameters, such as vascular resistance, compliance, and vessel cross-sectional area, known to be related to the development of hypertension. The proposed framework enables the prediction of hemodynamic quantities of interest, such as pressure and velocity, directly from sparse and noisy MRI measurements. We illustrate the effectiveness of this approach in two systemic arterial network geometries: an aorta with branching carotid artery and a maternal pelvic arterial network. For both cases, the model can reconstruct the provided measurements and infer parameters of interest. In the case of the maternal pelvic arteries, the model can make a distinction between the pregnancies destined to develop hypertension and those that remain normotensive, expressed through the value range of the predicted absolute pressure.

Biophysics↗

DOE OSTI2025

Improved Bayesian regularization of inverse problems in vibrations and acoustics using noise-only measurements

Here, this paper studies Tikhonov regularization (ridge regression) parameter selection for problems in vibrations and acoustics. The selection method is based on a popular Bayesian method, but it incorporates measurements of sensor noise. The regularization parameter is closely related to the ratio of system input energy to noise energy, so noise measurements inform the inference procedure and improve parameter identification. In cases where standard Bayesian regularization identifies zero as the optimal regularization parameter, noise measurements guarantee a unique nonzero optimum. Sufficient theoretical criteria are developed for this guarantee. The method is verified in even-determined and under-determined configurations in an acoustic source localization simulation and a vibration load identification experiment. It is shown to yield significant improvements over existing empirical Bayesian regularization. Improvements are larger in the even-determined case and smaller in the under-determined case, wherein the inverse solution is less sensitive to the regularization parameter.

42 ENGINEERING↗

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 OSTI2024

HPC Network Simulation Tuning via Automatic Extraction of Hardware Parameters

Popular HPC network interconnection simulators such as SST/macro provide a variety of configurable parameters to explore the design space of hardware components such as network interface cards (NIC), switches, and links among them. While such knobs provide flexibility to explore design trade-offs for novel hardware, manually configuring simulations for matching configurations of the existing hardware to focus on topology exploration can be cumbersome and error-prone, leading to widely inaccurate simulations. This challenge is compounded when specifications of various (proprietary) technologies are not readily available or intentionally omitted. In this work, we propose a framework to autotune the multiple network models’ simulation configurations within SST/macro using Tree-structured Parzen Estimator-based Bayesian optimization to observe the effect on simulation accuracy across different message regimes. These regimes consist of small to large message sizes and latency to bandwidth-bound messages. We provide a detailed analysis of the simulation error for four representative HPC systems. Our Bayesian optimization based autotuning framework for network models achieves a maximum of 5x improvement in accuracy over best-effort manual configurations based on available hardware specifications.

Simulation, autotuning↗

DOE OSTI2026

Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions

A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior $p$($q$,$n$|$D$) $\propto$ $\mathcal{L}$($D$|$q$,$n$)$p$(q)$p$($n$), where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p(n) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p(n) at arbitrary values of n, i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u, which projects away directions in n space that cannot appreciably alter $\mathcal{L}$. The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p(n) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n(z) of the galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Ground Heat Flux Reconstruction Using Bayesian Uncertainty Quantification Machinery and Surrogate Modeling

Ground heat flux (G 0 ) is a key component of the land-surface energy balance of high-latitude regions. Despite its crucial role in controlling permafrost degradation due to global warming, G 0 is sparsely measured and not well represented in the outputs of global scale model simulation. In this study, an analytical heat transfer model is tested to reconstruct G 0 across seasons using soil temperature series from field measurements, Global Climate Model, and climate reanalysis outputs. The probability density functions of ground heat flux and of model parameters are inferred using available G 0 data (measured or modeled) for snow-free period as a reference. When observed G 0 is not available, a numerical model is applied using estimates of surface heat flux (dependent on parameters) as the top boundary condition. These estimates (and thus the corresponding parameters) are verified by comparing the distributions of simulated and measured soil temperature at several depths. Aided by state-of-the-art uncertainty quantification methods, the developed G 0 reconstruction approach provides novel means for assessing the probabilistic structure of the ground heat flux for regional permafrost change studies.

54 ENVIRONMENTAL SCIENCES↗