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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 NTRS2008

Using Bayesian Networks for Candidate Generation in Consistency-based Diagnosis

Consistency-based diagnosis relies heavily on the assumption that discrepancies between model predictions and sensor observations can be detected accurately. When sources of uncertainty like sensor noise and model abstraction exist robust schemes have to be designed to make a binary decision on whether predictions are consistent with observations. This risks the occurrence of false alarms and missed alarms when an erroneous decision is made. Moreover when multiple sensors (with differing sensing properties) are available the degree of match between predictions and observations can be used to guide the search for fault candidates. In this paper we propose a novel approach to handle this problem using Bayesian networks. In the consistency- based diagnosis formulation, automatically generated Bayesian networks are used to encode a probabilistic measure of fit between predictions and observations. A Bayesian network inference algorithm is used to compute most probable fault candidates.

Narasimhan, Sriram↗

NASA NTRS2009

Understanding the Scalability of Bayesian Network Inference using Clique Tree Growth Curves

Bayesian networks (BNs) are used to represent and efficiently compute with multi-variate probability distributions in a wide range of disciplines. One of the main approaches to perform computation in BNs is clique tree clustering and propagation. In this approach, BN computation consists of propagation in a clique tree compiled from a Bayesian network. There is a lack of understanding of how clique tree computation time, and BN computation time in more general, depends on variations in BN size and structure. On the one hand, complexity results tell us that many interesting BN queries are NP-hard or worse to answer, and it is not hard to find application BNs where the clique tree approach in practice cannot be used. On the other hand, it is well-known that tree-structured BNs can be used to answer probabilistic queries in polynomial time. In this article, we develop an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN's non-root nodes to the number of root nodes, or (ii) the expected number of moral edges in their moral graphs. Our approach is based on combining analytical and experimental results. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for each set. For the special case of bipartite BNs, we consequently have two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, we systematically increase the degree of the root nodes in bipartite Bayesian networks, and find that root clique growth is well-approximated by Gompertz growth curves. It is believed that this research improves the understanding of the scaling behavior of clique tree clustering, provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms, and presents an aid for analytical trade-off studies of clique tree clustering using growth curves.

Mengshoel, Ole Jakob↗

NASA NTRS2012

Bayesian Analysis for Risk Assessment of Selected Medical Events in Support of the Integrated Medical Model Effort

The Exploration Medical Capability project is creating a catalog of risk assessments using the Integrated Medical Model (IMM). The IMM is a software-based system intended to assist mission planners in preparing for spaceflight missions by helping them to make informed decisions about medical preparations and supplies needed for combating and treating various medical events using Probabilistic Risk Assessment. The objective is to use statistical analyses to inform the IMM decision tool with estimated probabilities of medical events occurring during an exploration mission. Because data regarding astronaut health are limited, Bayesian statistical analysis is used. Bayesian inference combines prior knowledge, such as data from the general U.S. population, the U.S. Submarine Force, or the analog astronaut population located at the NASA Johnson Space Center, with observed data for the medical condition of interest. The posterior results reflect the best evidence for specific medical events occurring in flight. Bayes theorem provides a formal mechanism for combining available observed data with data from similar studies to support the quantification process. The IMM team performed Bayesian updates on the following medical events: angina, appendicitis, atrial fibrillation, atrial flutter, dental abscess, dental caries, dental periodontal disease, gallstone disease, herpes zoster, renal stones, seizure, and stroke.

Gilkey, Kelly M.↗

NASA NTRS2007

Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques

Uncertainty management has always been the key hurdle faced by diagnostics and prognostics algorithms. A Bayesian treatment of this problem provides an elegant and theoretically sound approach to the modern Condition- Based Maintenance (CBM)/Prognostic Health Management (PHM) paradigm. The application of the Bayesian techniques to regression and classification in the form of Relevance Vector Machine (RVM), and to state estimation as in Particle Filters (PF), provides a powerful tool to integrate the diagnosis and prognosis of battery health. The RVM, which is a Bayesian treatment of the Support Vector Machine (SVM), is used for model identification, while the PF framework uses the learnt model, statistical estimates of noise and anticipated operational conditions to provide estimates of remaining useful life (RUL) in the form of a probability density function (PDF). This type of prognostics generates a significant value addition to the management of any operation involving electrical systems.

Saha, Bhaskar↗

NASA NTRS2020

Using Bayesian Estimation to Quantify the Risks of Spaceflight

Complex PRA is the best method and current gold standard, as it allows us to reflect changes (improvements) in individual spacecraft system risks over time. Yet, Bayesian methods – using simple inputs – allowed us to get estimates that are in line with high-complexity PRA. Here Bayesian estimation acts as a “gut check” on PRA (supposing a “reasonable” prior is used). Frequentist calculations can overestimate P(failure), especially when total number of trials are few (e.g., after Challenger). In general, Bayesian probability estimation can be used in any risk assessment situation to integrate what we think we know ahead of time with what we observe over time.

Reynolds, Robert J.↗

NASA NTRS2022

Bayesian Rules of Thumb: Robust Uncertainty Quantification in Early Project Cost Estimation

Systems engineers often make use of cost Rules ofThumb in order to estimate cost during early phases of projectformulation. These Rules of Thumb typically take the form ofa sequence of percentages over which a total cost is allocatedacross NASA WBS elements. Rules of Thumb can then be usedto extrapolate cost from one or more known WBS elements tothe remaining unknown WBS elements, assisting early projectformulation architecture studies (such as those in JPL’s Team Xand A Team).A number of issues can arise when generating and using costRules of Thumb. For example, many records of project costsconsist of incomplete data. Typical methods of dealing withincomplete cost allocation data include (a) ignoring missionswith incomplete data, or (b) taking averages of the non-zero percentagesacross missions, but both of these methods can result inbiased estimates if the existence of incomplete data correlateswith total mission cost or any particular WBS element. Anothercommon example is cost reported in one or more incorrect WBSelements. This is especially prevalent in smaller missions whereit is more common for engineers to perform tasks that fall underthe purview of multiple WBS elements.Furthermore, a Rule of Thumb estimate is typically reported asa point estimate; there is no reported uncertainty around thepercentages used to generate an allocation. Even in the rarecase in which confidence intervals around mean percentages areprovided, there may be positive or negative correlations betweenWBS elements which can skew estimates.Here we attempt to address these problems by formulatingprobabilistic Rules of Thumb in which a distribution of allocationschemes, rather than a single allocation scheme, is generated.We use a bootstrap imputation method to simultaneouslyaccount for uncertainty in the missing data while using allavailable information contained in the dataset. The imputeddatasets are then input into a multivariate Bayesian modelwhich accounts for correlations between WBS elements andproperly accounts for uncertainty in the final Rule of Thumbpercentages and predictions. We describe the mathematicalmodel and provides snippets of R code utilizing the brms(Bayesian Regression Models using Stan) package. To illustratethis model, we generate a Bayesian Level 2 WBS Cost Rule ofThumb for MIDEX (Medium-Class Explorers) missions withdata extracted from NASA’s CADRe. We then compare thismethod’s performance with the classical Rule of Thumb method.

Hooke, Melissa A↗

DOE OSTI2022

Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in physics-based machine learning of dynamical (or Hamiltonian) systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture. But these types of architectures have not been applied to solve Bayesian inference problems efficiently. We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients. We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity and reduced integration errors. We integrate L-HNNs in NUTS and further propose an online error monitoring scheme to prevent sampling degeneracy in regions where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with online error monitoring consider several complex high-dimensional posterior densities and compare its performance to NUTS.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

A Bayesian approach to the long-baseline neutrino oscillation sensitivity of DUNE

The sensitivity of the Deep Underground Neutrino Experiment (DUNE) to neutrino oscillation is evaluated using a Bayesian Markov Chain Monte Carlo (MCMC) approach. This analysis uses the same underlying sensitivity inputs as previous DUNE studies [Eur. Phys. J. C 80, 978 (2020)], and therefore does not present updated DUNE sensitivities, but instead explores the additional inferences accessible using a Bayesian approach. We present four-dimensional posterior probability distributions of the oscillation parameters, highlighting the breadth of correlation in the parameter space of interest, especially between $\sin^2 θ_{23}$ and $\sin^2 θ_{13}$. We exploit the flexibility of the Bayesian framework to incorporate parameter constraints post hoc and assess the impact of applying a reactor short-baseline $θ_{13}$ constraint. A significant increase in the sensitivity to the $θ_{23}$ octant is found when including the constraint. Posterior distributions of derived quantities can be easily constructed from MCMC results. This work presents the first study of DUNE's sensitivity to the Jarlskog invariant, $J$, a quantity that provides a parametrisation-independent measure of charge-parity violation in the leptonic sector.

Abbaslu, Saeed [IPM, Tehran] (ORCID:00000003356771↗

DOE OSTI2021

Adaptive behavior and different thermal experiences of real people: A Bayesian neural network approach to thermal preference prediction and classification

Various observed and unquantifiable factors affect the thermal comfort of occupants in indoor environments and can lead to high uncertainty in the prediction and classification of their thermal preferences. The behavioral adaptation of occupants, by operating window systems for example, changes their thermal experience and expectations and therefore contributes to even higher prediction uncertainty. In this study, we applied a Bayesian neural network (BNN) algorithm to build a predictive model for occupant thermal preference using the ASHRAE Global Thermal Comfort Database II. The Bayesian method allows us to synthesize prior knowledge and available measurements into a unified modeling framework. It also offers a way to express and quantify uncertainty. Here we have performed a systematic study to test the efficiency and robustness of different BNN model configurations. In this study, the results show that the BNN model outperforms conventional thermal comfort models such as Predicted Mean Vote (PMV) and adaptive comfort model. The BNN model tends to produce more confident “prefer cooler” predictions with high possibility and low uncertainty. In contrast, the BNN model produces less certain predictions for “prefer no change” and “prefer warmer” across all occupants. Our findings suggest that linking occupants’ subjective evaluation measures and window opening/closing behavior to thermal comfort modeling effectively improves predictive performance.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Kinetic model development and Bayesian uncertainty quantification for the complete reduction of Fe-based oxygen carriers with CH 4 , CO, and H 2 for chemical looping combustion

In this work, three kinetic models are developed and calibrated for the complete multi-step reduction of an Fe-based oxygen carrier (OC) particle with CH 4 , CO, and H 2 , using data from thermogravimetric analysis. The complete reduction rate profiles exhibit complex dynamics whose trajectory is significantly different depending on the reducing gas. A Bayesian model building and parameter estimation framework is applied for simultaneous parameter and model structure uncertainty quantification. The final models show excellent agreement between model predictions and calibration data, as well as new data not used for calibration (for the reduction of the OC with CH 4 ). Parameter uncertainty is quantified by determining joint posterior distribution, and model structure uncertainty is addressed by incorporating Gaussian process stochastic functions (represented by Bayesian smoothing splines) into the kinetic models. The final kinetic models with discrepancy functions are readily employable in equation-oriented simulation and optimization platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Bayesian optimal experimental design for constitutive model calibration

Computational simulation is increasingly relied upon for high/consequence engineering decisions, which necessitates a high confidence in the calibration of and predictions from complex material models. However, the calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure—Interlaced Characterization and Calibration (ICC)—is introduced and demonstrated. Further, this framework leverages Bayesian optimal experimental design (BOED), which creates a line of communication between model calibration needs and data collection capabilities in order to optimize the information content gathered from the experiments for model calibration. Eventually, the ICC framework will be used in quasi real-time to actively control experiments of complex specimens for the calibration of a high-fidelity material model. This work presents the critical first piece of algorithm development and a demonstration in determining the optimal load path of a cruciform specimen with simulated data. Calibration results, obtained via Bayesian inference, from the integrated ICC approach are compared to calibrations performed by choosing the load path a priori based on human intuition, as is traditionally done. The calibration results are communicated through parameter uncertainties which are propagated to the model output space (i.e. stress–strain). In these exemplar problems, data generated within the ICC framework resulted in calibrated model parameters with reduced measures of uncertainty compared to the traditional approaches.

42 ENGINEERING↗

DOE OSTI2022

Posterior Regularized Bayesian Neural Network incorporating soft and hard knowledge constraints

Neural Networks (NNs) have been widely used in supervised learning due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. Furthermore, the experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.

14 SOLAR ENERGY↗

DOE OSTI2025

Bayesian optimization of PYTHIA 8 tunes

A new tune (set of model parameters) is found for the six most important parameters of the PYTHIA 8 final state parton shower and hadronization model using Bayesian optimization. The tune fits the Large Electron-Positron collider (LEPI) data from ALEPH better than the default tune in PYTHIA 8. To the best of our knowledge, we present the most comprehensive application of Bayesian optimization to the tuning of a parton shower and hadronization model using the LEPI data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments

Here, we present a novel stochastic approach to binary optimization suited for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. This formulation (a) is generally applicable to binary optimization problems with soft constraints and is ideal for OED and sensor placement problems; (b) does not require differentiability of the original objective function (e.g., a utility function in OED applications) with respect to the design variable, and thus it enables direct employment of sparsity-enforcing penalty functions such as $\ell_0$, without needing to utilize a continuation procedure or apply a rounding technique; (c) exhibits much lower computational cost than traditional gradient-based relaxation approaches; and (d) can be applied to both linear and nonlinear OED problems with proper choice of the utility function. The proposed approach is analyzed from an optimization perspective with detailed convergence analysis of the optimization approach and is also analyzed from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Challenges in Markov Chain Monte Carlo for Bayesian Neural Networks

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such challenges culminate to lack of convergence to the parameter posterior. Nevertheless, this paper shows that a nonconverged Markov chain, generated via MCMC sampling from the parameter space of a neural network, can yield via Bayesian marginalization a valuable posterior predictive distribution of the output of the neural network. Further, classification examples based on multilayer perceptrons showcase highly accurate posterior predictive distributions. The postulate of limited scope for MCMC developments in BNNs is partially valid; an asymptotically exact parameter posterior seems less plausible, yet an accurate posterior predictive distribution is a tenable research avenue.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Performing Bayesian Analyses With AZURE2 Using BRICK: An Application to the 7 Be System

Phenomenological R-matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist (χ 2 -based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, emcee, has been implemented for the R-matrix code AZURE2, creating the Bayesian R-matrix Inference Code Kit (BRICK). Bayesian uncertainty estimation has then been carried out for a simultaneous R-matrix fit of the 3 He (α,γ) 7 Be and 3 He (α,α) 3 He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state α-particle asymptotic normalization coefficients in 7 Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Hierarchical Bayesian method for mapping biogeochemical hot spots using induced polarization imaging

In floodplain environments, a naturally reduced zone (NRZ) is considered to be a common biogeochemical hot spot, having distinct microbial and geochemical characteristics. Although important for understanding their role in mediating floodplain biogeochemical processes, mapping the subsurface distribution of NRZs over the dimensions of a floodplain is challenging, as conventional wellbore data are typically spatially limited and the distribution of NRZs is heterogeneous. In this work, we present an innovative methodology for the probabilistic mapping of NRZs within a three-dimensional (3-D) subsurface domain using induced polarization imaging, which is a noninvasive geophysical technique. Measurements consist of surface geophysical surveys and drilling-recovered sediments at the U.S. Department of Energy field site near Rifle, CO (USA). Inversion of surface time domain-induced polarization (TDIP) data yielded 3-D images of the complex electrical resistivity, in terms of magnitude and phase, which are associated with mineral precipitation and other lithological properties. By extracting the TDIP data values colocated with wellbore lithological logs, we found that the NRZs have a different distribution of resistivity and polarization from the other aquifer sediments. To estimate the spatial distribution of NRZs, we developed a Bayesian hierarchical model to integrate the geophysical and wellbore data. In addition, the resistivity images were used to estimate hydrostratigraphic interfaces under the floodplain. Validation results showed that the integration of electrical imaging and wellbore data using a Bayesian hierarchical model was capable of mapping spatially heterogeneous interfaces and NRZ distributions thereby providing a minimally invasive means to parameterize a hydrobiogeochemical model of the floodplain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗