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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Discovering Planetary Nebula Geometries: Explorations with a Hierarchy of Models

Astronomical objects known as planetary nebulae (PNe) consist of a shell of gas expelled by an aging medium-sized star as it makes its transition from a red giant to a white dwarf. In many cases this gas shell can be approximately described as a prolate ellipsoid. Knowledge of the physics of ionization processes in this gaseous shell enables us to construct a model in three dimensions (3D) called the Ionization-Bounded Prolate Ellipsoidal Shell model (IBPES model). Using this model we can generate synthetic nebular images, which can be used in conjunction with Hubble Space Telescope (HST) images of actual PNe to perform Bayesian model estimation. Since the IBPES model is characterized by thirteen parameters, model estimation requires the search of a 13-dimensional parameter space. The 'curse of dimensionality,' compounded by a computationally intense forward problem, makes forward searches extremely time-consuming and frequently causes them to become trapped in local solutions. We find that both the speed and of the search can be improved by judiciously reducing the dimensionality of the search space. Our basic approach employs a hierarchy of models of increasing complexity that converges to the IBPES model. Earlier studies establish that a hierarchical sequence converges more quickly, and to a better solution, than a search relying only on the most complex model. Here we report results for a hierarchy of five models. The first three models treat the nebula as a 2D image, while the last two models explore its characteristics as a 3D object and enable us to characterize the physics of the nebula. This five-model hierarchy is applied to HST images of ellipsoidal PNe to estimate their geometric properties and gas density profiles.

Huyser, Karen A.↗
DOE OSTI2021

Case study: Accounting for response measurement error in fitting a regression model

This article presents a case study motivated by a plot of data that suggested an emerging trend that the authors were faced with explaining. When the measurement error of the data is accounted for, it turns out there was no real trend. Furthermore, this article shows how to use a Bayesian modeling approach to account for the measurement error.

42 ENGINEERING↗
DOE OSTI2025

Leveraging prior mean models for faster Bayesian optimization of particle accelerators

Tuning particle accelerators is a challenging and time-consuming task that can be automated and carried out efficiently using suitable optimization algorithms, such as model-based Bayesian optimization techniques. One of the major advantages of Bayesian algorithms is the ability to incorporate prior information about beam physics and historical behavior into the model used to make control decisions. In this work, we examine incorporating prior accelerator physics information into Bayesian optimization algorithms by utilizing fast executing, neural network models trained on simulated or historical datasets as prior mean functions in Gaussian process models. We show that in ideal cases, this technique substantially increases convergence speed to optimal solutions in high-dimensional tuning parameter spaces. Additionally, we demonstrate that even in non-ideal cases, where prior models of beam dynamics do not exactly match experimental conditions, the use of this technique can still enhance convergence speed. Finally, we demonstrate how these methods can be used to improve optimization in practical applications, such as transferring information gained from beam dynamics simulations to online control of the LCLS injector, and transferring knowledge gained from experimental measurements across different operating modes, such as accelerating different ion species at the ATLAS heavy ion accelerator.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Improved Statistical Analysis for the Neutrinoless Double-Beta Decay Matrix Element of 136Xe

Neutrinoless double beta decay nuclear matrix element (M0ν) for 136Xe was recently analyzed using a statistical approach (Phys. Rev. C 107, 045501 (2023)). In the analysis, three initial shell model effective Hamiltonians were randomly altered, and their results for 23 measured observables were used to infer credibility for the M0ν nuclear matrix element (NME) based on a Bayesian Model Averaging approach. In that analysis, a reasonable Gamow-Teller quenching factor of 0.7 was assumed for each starting effective Hamiltonian. Given that the result of the statistical analysis was sensible to this choice, we are here improving that analysis by assuming that the Gamow-Teller quenching factor is also randomly chosen within reasonabe limits for all three starting Hamiltonians. The outcomes are slightly higher expectation values and uncertainties for the M0ν NME.

Astronomy & Astrophysics↗
DOE OSTI2026

Technical Report for Bayesian Optimization and Reinforcement Learning for Beam Polarization Increase in the BNL Hadron Injectors

This project developed and evaluated physics-informed Bayesian learning and machine learning (ML)-based optimization methods for improving beam polarization preservation in the BNL hadron injector chain. The work focused on uncertainty-aware digital twin modeling, Bayesian calibration of accelerator simulations using beam measurements, and data-efficient optimization strategies including Bayesian optimization and reinforcement learning. These methods were applied to injector tuning and RF control problems in realistic accelerator settings to support improved operational robustness and readiness for RHIC operations and future Electron–Ion Collider facilities. No subject inventions were disclosed under this award.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

A Bayesian inferencing framework for ultrasound wave speed measurements in metal additive manufacturing

Process-related changes during metal additive manufacturing introduce microstructural variability in the material properties of printed parts, directly affecting component reliability. Accurate estimation of these property variations with part performance are essential for quality assurance. Ultrasound testing offers a non-destructive means to estimate mechanical properties and detect defects; however, conventional analysis methods often neglect the influence of microstructural variability, limiting their effectiveness. Here, this research presents a Bayesian inference technique for quantifying wave speed uncertainty from ultrasound measurements of metal additive manufactured parts. By integrating prior ultrasound data with a Bayesian model, the proposed approach generates posterior density estimates of wave speed that systematically account for manufacturing-induced variability and uncertainty. The novelty of this research lies in applying a Bayesian framework to analyze experimental ultrasound measurements within the context of metal additive manufacturing variability. The method enhances the accuracy of wave speed estimation by 64%, defect position by 50% and increases confidence associated with wave speed variance by 30% across different porosity levels, thereby providing a robust foundation for improved decision-making and increased reliability in additively manufactured components.

Additive manufacturing↗
DOE OSTI2026

NASA’s Pandora SmallSat Mission: Simulating the Impact of Stellar Photospheric Heterogeneity and Its Correction

Stellar photospheric heterogeneity is a dominant astrophysical systematic impacting exoplanet transmission spectroscopy. NASA’s Pandora SmallSat Mission is designed to address this challenge through contemporaneous visible-band photometry and near-infrared spectroscopy of exoplanet host stars. Here, we present an end-to-end simulation study quantifying Pandora’s ability to infer stellar photospheric properties and correct stellar contamination using out-of-transit observations. We construct eight representative stellar activity scenarios and generate 160 simulated Pandora datasets, incorporating time-dependent stellar spectra, instrument response, and noise. Given accurate models, Bayesian retrievals of joint visible photometry (0.4–0.7 μm) and near-infrared spectroscopy (0.9–1.6 μm, R ≈ 120) recover photospheric temperatures with typical uncertainties of ≈30 K, with no significant bias. Models with two spectral components (i.e., a quiescent photosphere and spots) are strongly favored in 95% of cases; one-component models are preferred when true spot filling factors fall below a detection threshold of ≈0.3%. We propagate the true and inferred stellar parameters to compute true, inferred, and residual contamination signals under physically motivated spot geometries. For simple spot distributions, contamination signals of 10 2 –10 3 ppm are reduced to ≲10 ppm—well below Pandora’s expected transmission spectroscopy precision (30–100 ppm). For more complex spot distributions, geometric degeneracies limit deterministic corrections, leaving residual contamination at the 10 3 ppm level that must be mitigated using additional constraints, such as spot-crossing events and joint stellar–planetary retrievals of transmission spectra. These results define regimes in which stellar contamination can be corrected from stellar observations alone and show how Pandora stellar observations can identify cases where additional information is required.

Astronomy and AstroPhysics↗
DOE OSTI2024

Assessing correlated truncation errors in modern nucleon-nucleon potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒⁢EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒⁢EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒⁢EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒⁢EFT NN potentials.

Bayesian methods↗
DOE OSTI2021

Simultaneous inference of the compressibility and inelastic response of tantalum under extreme loading

We study the deformation of tantalum under extreme loading conditions. Experimental velocity data are drawn from both ramp loading experiments on Sandia’s Z-machine and gas gun compression experiments. The drive conditions enable the study of materials under pressures greater than 100 GPa. We provide a detailed forward model of the experiments including a model of the magnetic drive for the Z-machine. Utilizing these experiments, we simultaneously infer several different types of physically motivated parameters describing equation of state, plasticity, and anelasticity via the computational device of Bayesian model calibration. Characteristics of the resulting calculated posterior distributions illustrate relationships among the parameters of interest via the degree of cross correlation. The calibrated velocity traces display good agreement with the experiments up to experimental uncertainty as well as improvement over previous calibrations. Examining the Z-shots and gun-shots together and separately reveals a trade-off between accuracy and transferability across different experimental conditions. Implications for model calibration, limitations from model form, and suggestions for improvements are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bayesian estimation of the $S$ factor and thermonuclear reaction rate for 16 O(p, γ) 17 F

The 16 O(p, γ) 17 F reaction is the slowest hydrogen-burning process in the CNO mass region. Its thermonuclear rate sensitively impacts predictions of oxygen isotopic ratios in a number of astrophysical sites, including AGB stars. The reaction has been measured several times at low bombarding energies using a variety of techniques. The most recent evaluated experimental rates have a reported uncertainty of about 7.5% below 1 GK. However, the previous rate estimate represents a best guess only and was not based on rigorous statistical methods. We apply a Bayesian model to fit all reliable 16 O(p, γ) 17 F cross section data, and take into account independent contributions of statistical and systematic uncertainties. The nuclear reaction model employed is a single-particle potential model involving a Woods-Saxon potential for generating the radial bound state wave function. The model has three physical parameters, the radius and diffuseness of the Woods-Saxon potential, and the asymptotic normalization coefficients (ANCs) of the final bound state in 17 F. Here, we find that performing the Bayesian S -factor fit using ANCs as scaling parameters has a distinct advantage over adopting spectroscopic factors instead. Based on these results, we present the first statistically rigorous estimation of experimental 16 O(p, γ) 17 F reaction rates, with uncertainties (±4.2%) of about half the previously reported values.

6 ≤ A ≤ 19↗
DOE OSTI2021

A Bayesian Calibration Framework with Embedded Model Error for Model Diagnostics

We study the utility and performance of a Bayesian model error embedding construction in the context of molecular dynamics modeling of metallic alloys, where we embed model error terms in existing interatomic potential model parameters. To alleviate the computational burden of this approach, we propose a framework combining likelihood approximation and Gaussian process surrogates. Here we leverage sparse Gaussian process techniques to construct a hierarchy of increasingly accurate but more expensive surrogate models. This hierarchy is then exploited by multilevel Markov chain Monte Carlo methods to efficiently sample from the target posterior distribution. We illustrate the utility of this approach by calibrating an interatomic potential model for a family of gold-copper alloys. In particular, this case study highlights effective means for dealing with computational challenges with Bayesian model error embedding in large-scale physical models, and the utility of embedded model error for model diagnostics.

Bayesian inference↗
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 OSTI2023

Bayesian filtering for model predictive control of stochastic gene expression in single cells

This study describes a method for controlling the production of protein in individual cells using stochastic models of gene expression. By combining modern microscopy platforms with optogenetic gene expression, experimentalists are able to accurately apply light to individual cells, which can induce protein production. Here we use a finite state projection based stochastic model of gene expression, along with Bayesian state estimation to control protein copy numbers within individual cells. We compare this method to previous methods that use population based approaches. We also demonstrate the ability of this control strategy to ameliorate discrepancies between the predictions of a deterministic model and stochastic switching system.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference↗
DOE OSTI2025

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Multiscale influenza forecasting

Abstract Influenza forecasting in the United States (US) is complex and challenging due to spatial and temporal variability, nested geographic scales of interest, and heterogeneous surveillance participation. Here we present Dante, a multiscale influenza forecasting model that learns rather than prescribes spatial, temporal, and surveillance data structure and generates coherent forecasts across state, regional, and national scales. We retrospectively compare Dante’s short-term and seasonal forecasts for previous flu seasons to the Dynamic Bayesian Model (DBM), a leading competitor. Dante outperformed DBM for nearly all spatial units, flu seasons, geographic scales, and forecasting targets. Dante’s sharper and more accurate forecasts also suggest greater public health utility. Dante placed 1st in the Centers for Disease Control and Prevention’s prospective 2018/19 FluSight challenge in both the national and regional competition and the state competition. The methodology underpinning Dante can be used in other seasonal disease forecasting contexts having nested geographic scales of interest.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Ecological connectivity and habitat loss shape patterns of genetic diversity in a threatened salamander

Context The maintenance of genetic diversity is essential for preserving adaptive potential in populations, yet it is increasingly threatened by landscape alteration. The field of landscape genetics offers a framework for assessing how patch-level landscape conditions, modeled at multiple scales, influence genetic diversity. Objectives We sought to assess how local environmental features and connectivity influence genetic diversity across 74 four-toed salamander (Hemidactylium scutatum) breeding wetlands in the southeastern United States. Methods Using next-generation sequencing data and hierarchical Bayesian models, we examined genome-wide heterozygosity in relation to local landscape features and ecological connectivity. We also assessed the scale of effect of landscape features and tested for temporal lag effects. Results Genetic diversity was lower in wetlands with higher levels of historic deforestation and lower connectivity. An interaction between deforestation and connectivity indicated that deforestation had stronger negative effects in isolated wetlands but weaker effects in well-connected wetlands. Accounting for scale of effect and temporal lags was critical for detecting these relationships. Conclusions Our analyses highlight the importance of assessing the spatial scale (scale of effect) and temporal lag of landscape features to detect key drivers of genetic diversity. In line with population genetic theory, our results indicate that the genetic consequences of habitat loss do not affect populations uniformly and are most severe in isolated populations where gene flow cannot buffer against loss of diversity. Altogether, we highlight the importance of considering the interaction of habitat loss and connectivity in conservation genetic management.

Hemidactylium scutatum↗
DOE OSTI2023

Assessing the ultracentral flow puzzle in hydrodynamic modeling of heavy-ion collisions

An outstanding problem in heavy-ion collisions is the inability for models to accurately describe ultra-central experimental flow data, despite that being precisely the regime where a hydrodynamic description should be most applicable. Here, we reassess the status of this puzzle by computing the flow in ultra-central collisions obtained from multiple recent Bayesian models that were tuned to various observables in different collision systems at typical centralities. While central data can now be described with better accuracy than in previous calculations, tension with experimental observation remains and worsens as one goes to ultra-central collisions. Tuning the model parameters cannot remove this tension without destroying the fit at other centralities. As such, new elements are likely needed in the standard modeling of heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗