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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Bayesian Cross-matching of High Proper-motion Stars in Gaia DR2 and Photometric Metallicities for ∼1.7 million K and M Dwarfs

We present a Bayesian method to cross-match 5,827,988 high proper-motion Gaia sources (μ > 40 mas yr{sup −1}) to various photometric surveys: Two Micron All Sky Survey, AllWISE data release from the Wide-field Infrared Explorer (WISE) mission, Galaxy Evolution Explorer, Radial Velocity Experiment, Sloan Digital Sky Survey, and Panoramic Survey Telescope and Rapid Response System (Pan-STARRS). To efficiently associate these objects across catalogs, we develop a technique that compares the multidimensional distribution of all sources in the vicinity of each Gaia star to a reference distribution of random field stars obtained by extracting all sources in a region on the sky displaced 2′. This offset preserves the local field stellar density and magnitude distribution, allowing us to characterize the frequency of chance alignments. The resulting catalog with Bayesian probabilities >95% has a marginally higher match rate than current internal Gaia data release 2 (DR2) matches for most catalogs. However, a significant improvement is found with Pan-STARRS, where ∼99.8% of the sample within the Pan-STARRS footprint is recovered, as compared to a low ∼20.8% in Gaia DR2. Using these results, we train a Gaussian process regressor to calibrate two photometric metallicity relationships. For dwarfs of 3500 < T{sub eff} < 5280 K, we use metallicity values of 4378 stars from the Apache Point Observatory Galactic Evolution Experiment and Hejazi et al. to calibrate the relationship, producing results with a 1σ precision of 0.12 dex and few systematic errors. We then indirectly infer the metallicity of 4018 stars with 2850 < T{sub eff} < 3500 K, which are wide companions of primaries whose metallicities are estimated with our first regressor, to produce a relationship with a 1σ precision of 0.21 dex and significant systematic errors. Additional work is needed to better remove unresolved binaries from this second sample to reduce these systematic errors.

47 OTHER INSTRUMENTATION↗
NASA NTRS2004

A Bayesian approach to tracking patients having changing pharmacokinetic parameters

This paper considers the updating of Bayesian posterior densities for pharmacokinetic models associated with patients having changing parameter values. For estimation purposes it is proposed to use the Interacting Multiple Model (IMM) estimation algorithm, which is currently a popular algorithm in the aerospace community for tracking maneuvering targets. The IMM algorithm is described, and compared to the multiple model (MM) and Maximum A-Posteriori (MAP) Bayesian estimation methods, which are presently used for posterior updating when pharmacokinetic parameters do not change. Both the MM and MAP Bayesian estimation methods are used in their sequential forms, to facilitate tracking of changing parameters. Results indicate that the IMM algorithm is well suited for tracking time-varying pharmacokinetic parameters in acutely ill and unstable patients, incurring only about half of the integrated error compared to the sequential MM and MAP methods on the same example.

Bayes Theorem↗
NASA NTRS1972

Bayesian recursive image estimation.

The enhancement of images that are characterized only by statistical data where the picture contains additive noise is considered. The random process representing the output of the scanner is characterized by the output of a dynamic system with white noise input. The dynamic system describes a first-order vector-Markov process. The procedure of Kalman filtering is then utilized to recursively determine the minimum mean-square error estimate of the image. The result is then extended to obtain the smoothing of the data.

Nahi, N. E.↗
DOE OSTI2021

Towards robust autonomous impedance spectroscopy analysis: A calibrated hierarchical Bayesian approach for electrochemical impedance spectroscopy (EIS) inversion

Distribution-based analyses, such as the distribution of relaxation times (DRT) and the distribution of diffusion times (DDT), present model-free alternatives to equivalent circuit modeling for analysis of electrochemical impedance spectroscopy (EIS) data. However, reconstructing such distributions from noisy impedance data is an ill-posed problem that must be solved with specialized inversion algorithms, requiring careful control and tuning. Furthermore, most inversion algorithms developed to date can only solve problems of limited complexity. Herein, we present a new hierarchical Bayesian method for EIS inversion, leveraging efficient algorithms for optimization and Hamiltonian Monte Carlo (HMC) sampling to solve models of arbitrary complexity. We overcome the challenge of ad-hoc parameter tuning by encoding intrinsic characteristics of the DRT and DDT into flexible prior distributions and “pre-calibrating” the model to simulated data. This approach is versatile, highly robust to noise, and provides quantitative estimates of both the error structure of the data and the uncertainty in the recovered distributions. The model is validated with simulated data to demonstrate accurate recovery of the DRT and the DDT. The method also shows promise for simultaneous recovery of multiple distributions, raising the intriguing possibility of semi-autonomous EIS analysis and ad-hoc model construction. Finally, the practical utility of the method is illustrated with experimental data. Throughout, we draw comparisons to several recently published EIS inversion methodologies.

36 MATERIALS SCIENCE↗
DOE OSTI2026

A dendritic strontium river isoscape for fisheries applications in the Sacramento River basin, California, USA

Objective Understanding the origins and movements of fish is fundamental to effective conservation and fisheries management. Strontium isotope ratios ( 87 Sr/ 86 Sr) in otoliths provide a powerful tracer of natal origin and migratory pathways. However, existing 87 Sr/ 86 Sr isoscapes for the Sacramento River basin, an ecosystem that supports ecologically and economically important salmon populations, rely on discrete classification approaches that overlook unsampled habitats and do not incorporate spatial uncertainty. Our objective was to develop a continuous, network-explicit 87 Sr/ 86 Sr isoscape with quantified uncertainty to fill in data gaps and enable probabilistic assignments of fish origin and movement. Methods We used river water 87 Sr/ 86 Sr data from 106 sites (1997–2021) to develop spatial stream network models that use dendritic connectivity and watershed characteristics (lithology, bedrock age, and land cover) to predict river water 87 Sr/ 86 Sr throughout the basin. Models were fitted using maximum and restricted likelihood and were evaluated via Akaike’s information criterion and leave-one-out cross validation. We produced both historical (pre-dam) and present-day (below-dam) isoscapes, delineated uncertainty-informed isotopic ranges using k -means clustering, and applied a proof-of-concept Bayesian assignment to estimate natal origins and early rearing habitats for two endangered winter-run Chinook Salmon Oncorhynchus tshawytscha. Results Cross validation indicated strong performance of the 87 Sr/ 86 Sr model (leave-one-out cross validation: R 2 = 0.91; root mean square error = 0.0005). Uncertainty-informed clustering identified 19 isotopic “suites” (reaches with indistinguishable 87 Sr/ 86 Sr values) in present-day anadromous habitats and 25 suites in the historical network. Example natal and early rearing assignments included predictions that challenged expectations for juvenile salmon migration based on predicted river 87 Sr/ 86 Sr compositions. Conclusions This study developed a continuous, network-explicit 87 Sr/ 86 Sr isoscape that integrates existing river data to predict 87 Sr/ 86 Sr in unsampled reaches and the likely achievable range and resolution of otolith-based origin and life history inference. The resulting river isoscape provides a valuable tool to predict salmon movements and identify habitats supporting their survival and growth that otherwise might remain undetected. Coupling these predictions with complementary approaches that ground-truth juvenile presence (e.g., targeted fish surveys) represents an important step toward science-informed restoration and management of critical habitats throughout the Sacramento River basin.

Environmental sciences↗
NASA NTRS1980

Evaluation of Bayesian Sequential Proportion Estimation Using Analyst Labels

The author has identified the following significant results. A total of ten Large Area Crop Inventory Experiment Phase 3 blind sites and analyst-interpreter labels were used in a study to compare proportional estimates obtained by the Bayes sequential procedure with estimates obtained from simple random sampling and from Procedure 1. The analyst error rate using the Bayes technique was shown to be no greater than that for the simple random sampling. Also, the segment proportion estimates produced using this technique had smaller bias and mean squared errors than the estimates produced using either simple random sampling or Procedure 1.

Lennington, R. K.↗
NASA NTRS1977

Orbit determination accuracies using satellite-to-satellite tracking

The uncertainty in relay satellite sate is a significant error source which cannot be ignored in the reduction of satellite-to-satellite tracking data. Based on simulations and real data reductions, it is numerically impractical to use simultaneous unconstrained solutions to determine both relay and user satellite epoch states. A Bayesian or least squares estimation technique with an a priori procedure is presented which permits the adjustment of relay satellite epoch state in the reduction of satellite-to-satellite tracking data without the numerical difficulties introduced by an ill-conditioned normal matrix.

Vonbun, F. O.↗
DOE OSTI2022

Quantifying modeling uncertainty in simplified beam models for building response prediction

The use of simple models for response prediction of building structures is preferred in earthquake engineering for risk evaluations at regional scales, as they make computational studies more feasible. The primary impediment in their gainful use presently is the lack of viable methods for quantifying (and reducing upon) the modeling errors/uncertainties they bear. This study presents a Bayesian calibration method wherein the modeling error is embedded into the parameters of the model. Here, the method is specifically described for coupled shear-flexural beam models here, but it can be applied to any parametric surrogate model. The major benefit the method offers is the ability to consider the modeling uncertainty in the forward prediction of any degree-of-freedom or composite response regardless of the data used in calibration. The method is extensively verified using two synthetic examples. In the first example, the beam model is calibrated to represent a similar beam model but with enforced modeling errors. In the second example, the beam model is used to represent the detailed finite element model of a 52-story building. Both examples show the capability of the proposed solution to provide realistic uncertainty estimation around the mean prediction.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Comparing traditional and Bayesian approaches to ecological meta‐analysis

Abstract Despite the wide application of meta‐analysis in ecology, some of the traditional methods used for meta‐analysis may not perform well given the type of data characteristic of ecological meta‐analyses. We reviewed published meta‐analyses on the ecological impacts of global climate change, evaluating the number of replicates used in the primary studies ( n i ) and the number of studies or records ( k ) that were aggregated to calculate a mean effect size. We used the results of the review in a simulation experiment to assess the performance of conventional frequentist and Bayesian meta‐analysis methods for estimating a mean effect size and its uncertainty interval. Our literature review showed that n i and k were highly variable, distributions were right‐skewed and were generally small (median n i = 5, median k = 44). Our simulations show that the choice of method for calculating uncertainty intervals was critical for obtaining appropriate coverage (close to the nominal value of 0.95). When k was low (<40), 95% coverage was achieved by a confidence interval (CI) based on the t distribution that uses an adjusted standard error (the Hartung–Knapp–Sidik–Jonkman, HKSJ), or by a Bayesian credible interval, whereas bootstrap or z distribution CIs had lower coverage. Despite the importance of the method to calculate the uncertainty interval, 39% of the meta‐analyses reviewed did not report the method used, and of the 61% that did, 94% used a potentially problematic method, which may be a consequence of software defaults. In general, for a simple random‐effects meta‐analysis, the performance of the best frequentist and Bayesian methods was similar for the same combinations of factors ( k and mean replication), though the Bayesian approach had higher than nominal (>95%) coverage for the mean effect when k was very low ( k < 15). Our literature review suggests that many meta‐analyses that used z distribution or bootstrapping CIs may have overestimated the statistical significance of their results when the number of studies was low; more appropriate methods need to be adopted in ecological meta‐analyses.

Pappalardo, Paula↗
NASA NTRS2019

Health Management and Prognostics for Electric Aircraft Powertrain

W and c Any air borne vehicle needs incorporating safety as key parameter of measure, and inclusion of autonomy raises the critical need for safety under autonomous operations. Management of faults and component degradation is key as complexity in autonomous operations grow over the period of time. Therefore, in addition to basic operational requirements, an autonomous electric vehicle should be able to make accurate estimates of its current system health and take the correct decisions to complete its mission successfully. Real-time safety and state-awareness tools are therefore essential for the vehicle to be able to reach its destination in a safe and successful manner. The need for safety assurance and health management capabilities is particularly relevant for aircraft electric propulsion systems, which are relatively new and with limited historical to learn. They are critical systems requiring high power density along with reliability, resilience, efficient management of weight, and operational costs. A model- based fault diagnosis and prognostics approach of complex critical systems can successfully accomplish the safety and state awareness goal for such electric propulsion systems, enabling autonomous decision making capability for safe and efficient operation. To identify critical components in the system a Qualitative Bayesian approach using FMECA is implemented. This requires the assessment of some quantities representing the state of the electric unmanned aerial systems (e-UAS), as well as look-ahead forecasts of such states during the entire flight, presented in form of safety metrics (SM). In-service data and performance data gathered from degraded components sup- ports diagnostic and prognostic methods for these systems, but this data can be difficult to obtain as weight and packaging restrictions reduce redundancy and instrumentation on-board the vehicle. Therefore, an model-based framework should be capable or operating with limited data. In addition to data scarcity, the variability of such complex critical systems re- quires the model-based framework to reason in the presence of uncertainty, such as sensor noise, and modeling imperfections. Quantification of errors and uncertainties in the measured states and quantities is therefore a fundamental step for a precise estimation of such SMs; un-modeled uncertainty may result in erroneous state assessment and un- reliable predictions of future states of e-UAVs. Typical, centralized model-based schemes suffer from inherent disadvantages such as computational complexity, single point of failure, and scalability issues, and therefore may fail in such a complex scenario. This paper presents a methodology for developing a system level diagnostics and prognostics approach using a Qualitative Bayesian FMECA approach along with a formal uncertainty management framework for an e-UAS. In this work we demonstrate the efficacy of the framework to predict effects of sub-system level degradation on vehicle operation incorporating uncertainty management to predict future behavior under different operating conditions.

Kulkarni, Chetan↗
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 OSTI2026

Advanced Semi-Supervised Learning with Uncertainty Estimation for Phase Identification in Distribution Systems

The integration of advanced metering infrastructure (AMI) into power distribution networks generates valuable data for tasks such as phase identification; however, the limited and unreliable availability of labeled data in the form of customer phase connectivity presents challenges. To address this issue, we propose a semi-supervised learning (SSL) framework that effectively leverages labeled and unlabeled data. Our approach incorporates self-training, label spreading, and Bayesian neural networks (BNNs) to enhance phase identification with AMI data. Our method uses an ensemble of multilayer perceptron classifiers in a self-training setup, iteratively adding high-confidence pseudo-labels to improve robustness. We also apply label spread to propagate labels based on data similarity, which enhances generalization across diverse distributions. In addition, we employ a BNNs with uncertainty estimation, boosting confidence in predictions and reducing phase identification errors. In our case study, we achieved approximately 98% +/- 0.08 accuracy with uncertainty using minimal and unreliable labeled data from a real U.S. utility, Duquesne Light Company. Our SSL approach, combined with uncertainty estimation, provides an efficient solution for phase identification in AMI data, ultimately improving the reliability of smart grid applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Advanced Semi-Supervised Learning With Uncertainty Estimation for Phase Identification in Distribution Systems

The integration of advanced metering infrastructure (AMI) into power distribution networks generates valuable data for tasks such as phase identification; however, the limited and unreliable availability of labeled data in the form of customer phase connectivity presents challenges. To address this issue, we propose a semi-supervised learning (SSL) framework that effectively leverages labeled and unlabeled data. Our approach incorporates self-training, label spreading, and Bayesian neural networks (BNNs) to enhance phase identification with AMI data. Our method uses an ensemble of multilayer perceptron classifiers in a self-training setup, iteratively adding high-confidence pseudo-labels to improve robustness. We also apply label spread to propagate labels based on data similarity, which enhances generalization across diverse distributions. In addition, we employ a BNNs with uncertainty estimation, boosting confidence in predictions and reducing phase identification errors. In our case study, we achieved approximately 98% +/- 0.08 accuracy with uncertainty using minimal and unreliable labeled data from a real U.S. utility, Duquesne Light Company. Our SSL approach, combined with uncertainty estimation, provides an efficient solution for phase identification in AMI data, ultimately improving the reliability of smart grid applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A novel probabilistic regression model for electrical peak demand estimate of commercial and manufacturing buildings

Due to the high cost of electricity in commercial and industrial sectors, demand forecast models have gained increasing attention. However, there are two unresolved issues: (1) Models are not adaptable when exposed to previously unknown data (2) The value of regression methods vs. state-of-the-art machine learning models has not been made apparent before. This study’s goal is to develop probabilistic demand estimation models. Herein, we propose a probabilistic Bayesian regression framework that can not only estimate future demands with high accuracy but also be updated once new information is available. By applying the proposed algorithm to two real-world case studies (commercial and manufacturing), we show a 40.3% and 30.8% improvement in terms of mean absolute error for the two cases. Moreover, the proposed technique outperforms powerful machine learning approaches, including support vector machine by 10.39%, random forest by 6.17%, and multilayer perceptron by 9.14% in terms of mean absolute percentage error.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2016

Modeling Forest Biomass and Growth: Coupling Long-Term Inventory and Lidar Data

Combining spatially-explicit long-term forest inventory and remotely sensed information from Light Detection and Ranging (LiDAR) datasets through statistical models can be a powerful tool for predicting and mapping above-ground biomass (AGB) at a range of geographic scales. We present and examine a novel modeling approach to improve prediction of AGB and estimate AGB growth using LiDAR data. The proposed model accommodates temporal misalignment between field measurements and remotely sensed data-a problem pervasive in such settings-by including multiple time-indexed measurements at plot locations to estimate AGB growth. We pursue a Bayesian modeling framework that allows for appropriately complex parameter associations and uncertainty propagation through to prediction. Specifically, we identify a space-varying coefficients model to predict and map AGB and its associated growth simultaneously. The proposed model is assessed using LiDAR data acquired from NASA Goddard's LiDAR, Hyper-spectral & Thermal imager and field inventory data from the Penobscot Experimental Forest in Bradley, Maine. The proposed model outperformed the time-invariant counterpart models in predictive performance as indicated by a substantial reduction in root mean squared error. The proposed model adequately accounts for temporal misalignment through the estimation of forest AGB growth and accommodates residual spatial dependence. Results from this analysis suggest that future AGB models informed using remotely sensed data, such as LiDAR, may be improved by adapting traditional modeling frameworks to account for temporal misalignment and spatial dependence using random effects.

Babcock, Chad↗
DOE OSTI2024

PINN surrogate of Li-ion battery models for parameter inference, Part II: Regularization and application of the pseudo-2D model

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of ~2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. Finally, in the low-data availability scenario, the testing error was estimated to ~2 mV for the SPM surrogate and ~10 mV for the P2D surrogate which could be mitigated with additional data.

25 ENERGY STORAGE↗
DOE OSTI2022

Characterizing and Mitigating Intraday Variability: Reconstructing Source Structure in Accreting Black Holes with mm-VLBI

The extraordinary physical resolution afforded by the Event Horizon Telescope has opened a window onto the astrophysical phenomena unfolding on horizon scales in two known black holes, M87* and Sgr A*. However, with this leap in resolution has come a new set of practical complications. Sgr A* exhibits intraday variability that violates the assumptions underlying Earth aperture synthesis, limiting traditional image reconstruction methods to short timescales and data sets with very sparse (u, v) coverage. We present a new set of tools to detect and mitigate this variability. We develop a data-driven, model-agnostic procedure to detect and characterize the spatial structure of intraday variability. This method is calibrated against a large set of mock data sets, producing an empirical estimator of the spatial power spectrum of the brightness fluctuations. We present a novel Bayesian noise modeling algorithm that simultaneously reconstructs an average image and statistical measure of the fluctuations about it using a parameterized form for the excess variance in the complex visibilities not otherwise explained by the statistical errors. These methods are validated using a variety of simulated data, including general relativistic magnetohydrodynamic simulations appropriate for Sgr A* and M87*. We find that the reconstructed source structure and variability are robust to changes in the underlying image model. We apply these methods to the 2017 EHT observations of M87*, finding evidence for variability across the EHT observing campaign. The variability mitigation strategies presented are widely applicable to very long baseline interferometry observations of variable sources generally, for which they provide a data-informed averaging procedure and natural characterization of inter-epoch image consistency.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Restricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter (β) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

97 MATHEMATICS AND COMPUTING↗