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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A scalable variational method for estimating the latent infection-rate field of an outbreak

In this paper, we explore whether the infection-rate of a disease can serve as a robust monitoring variable in epidemiological surveillance algorithms. The infection-rate is dependent on population mixing patterns that do not vary erratically day-to-day; in contrast, daily case-counts used in contemporary surveillance algorithms are corrupted by reporting errors. The technical challenge lies in estimating the latent infection-rate from case-counts. Here we devise a Bayesian method to estimate the infection-rate across multiple adjoining areal units, and then use it, via an anomaly detector, to discern a change in epidemiological dynamics. We extend an existing model for estimating the infection-rate in an areal unit by incorporating a Markov random field model, so that we may estimate infection-rates across multiple areal units, while preserving spatial correlations observed in the epidemiological dynamics. To carry out the high-dimensional Bayesian inverse problem, we develop an implementation of mean-field variational inference specific to the infection model and integrate it with the random field model to incorporate correlations across counties. The method is tested on estimating the COVID-19 infection-rates across all 33 counties in New Mexico using data from the summer of 2020, and then employing them to detect the arrival of the Fall 2020 COVID-19 wave. We perform the detection using a temporal algorithm that is applied county-by-county. We also show how the infection-rate field can be used to cluster counties with similar epidemiological dynamics.

60 APPLIED LIFE SCIENCES↗
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

ELG×LRG Distribution through Dark Matter Halo Dynamics

We investigate the clustering and halo occupation distribution (HOD) of DESI Y1 emission-line (ELGs) and luminous red (LRGs) galaxies at 0.8 < z < 1.1, including their cross-correlation (ELG×LRG), using the A BACUS S UMMIT suite and a new Halo Occupation Model (H OME ) for galaxy multitracers. This integrates intrahalo dynamics, halo exclusion, and quenching, bridging insights from hydrodynamical, HOD, abundance-matching, and semianalytic studies. Leveraging full phase-space information from the Uchuu N-body simulation, and sampling satellites from dark-matter particle positions via physically motivated prescriptions, Home reproduces the anisotropic clustering down to s = 200 h −1 kpc with unprecedented accuracy. Model parameters are inferred solely from two-point statistics using a two-level Bayesian framework, yielding high-fidelity ELG, LRG, and cross-reference catalogs. We find that satellite ELGs behave as incoherent flows within their parent halos, dominating the clustering below 4 h −1 Mpc. The HOD from the best-fit Home has the following properties: (i) 90.50% (85.91%) of ELGs (LRGs) are central galaxies without satellites, residing in halos of M vir ∼ 6.6 × 10 11 (1.2 × 10 13 ) h −1 M ⊙ ; (ii) the ELG×LRG cross-correlation is governed by central-central pairs and shaped by halo exclusion on 2–5 h −1 Mpc scales; (iii) 9.50% (14.09%) of ELGs (LRGs) are satellites, of which 1.09% (3.52%) inhabit halos with a central galaxy of the same species in a maximally conformal configuration, 7.02% (0.005%) orbit complementary hosts in a minimally conformal state, and 0.58% (10.57%) are orphans. The high sensitivity of Home precisely captures the dynamics of satellites in different host environments, opening a promising avenue for understanding systematics and the dynamical nature of dark matter, potentially distinguishing gravity models.

Favole, Ginevra [Universidad de La Laguna (Spain);↗
DOE OSTI2026

Bayesian discovery of optimal reduced order models from mechanistic and experimental data: A case study of Pd penetration in TRISO fuels using BISON

TRistructural ISOtropic (TRISO) particles rely on a silicon carbide (SiC) layer as the primary structural material and barrier to metallic fission products (FPs) release. Accurate prediction of palladium (Pd) transport and penetration is therefore critical for qualifying TRISO fuels for advanced reactors. The empirical correlation for Pd penetration in BISON is derived from historical particle-fuel data, but cannot explain the large scatter in the experimental data that arises from varying experimental conditions. To aid fuel qualification, we previously developed a mechanistic reduced order model (ROM) using BISON that resolves these dependencies. Here, in this work we build on that mechanistic ROM and perform validation and quantify its uncertainty using Bayesian uncertainty quantification (UQ). calibration against a suite of in-pile and out-of-pile experiments spanning particle compositions, geometries, and operating conditions, and we benchmark it against the empirical correlation. Bayesian UQ identifies influential parameters, calibrates them to data, and yields predictive intervals. Results show that while the empirical correlation can be tuned to fit a single experiment type, it transfers poorly; the mechanistic ROM sustains accuracy with credible uncertainty across disparate conditions. This demonstrates a practical path—via Bayesian UQ applied to mechanistic ROMs—to leverage single-effect experiments for inferring in-reactor behavior and supporting TRISO fuel qualification.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Neural Posterior Estimation for Scalable and Accurate Inverse Parameter Inference in Li-Ion Batteries

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter estimation via Bayesian calibration, diagnostics can account for the uncertainty due to model fitness, data noise, and the observability of any given parameter. However, Bayesian calibration in Li-ion batteries using electrochemical data is computationally intensive even when using a fast surrogate in place of physics-based models, requiring many thousands of model evaluations. A fully amortized alternative is neural posterior estimation (NPE). NPE shifts the computational burden from the parameter estimation step to data generation and model training, reducing the parameter estimation time from minutes to milliseconds, enabling real-time applications. The present work shows that NPE can infer parameters equally or more accurately than Bayesian calibration, even if it leads to higher voltage reconstruction errors. We also demonstrate that the higher computational costs for data generation are tractable even in high-dimensional cases (ranging from 6 to 27 estimated parameters). The NPE method also offers several interpretability advantages over Bayesian calibration, such as local parameter sensitivity to specific regions of the voltage curve. The NPE method is demonstrated using an experimental fast charge dataset, with parameter estimates validated against measurements of loss of lithium inventory and loss of active material. The implementation is made available in a companion repository (https://github.com/NatLabRockies/BatFIT).

25 ENERGY STORAGE↗
DOE OSTI2025

Aided Active Learning (AAL) for Enhanced Critical Heat Flux Prediction

Accurate prediction of critical heat flux (CHF) is crucial for the safe and efficient operation of nuclear reactors. Traditional CHF modeling methods often require extensive experimental data, which are hard to obtain. This study introduces the Aided Active Learning (AAL) framework, which strategically minimizes data requirements without sacrificing model accuracy. Unlike conventional Active Learning (AL), AAL introduces an additional step of randomly selecting a subset from the sample pool before applying the query strategy. To evaluate the performance of AAL, two query strategies—uncertainty-based sampling and error-reduction sampling—were evaluated across the following models: random forest (RF), feedforward neural network (FNN), and variational feedforward neural network (vFNN). The proposed framework demonstrated that AAL effectively reduces the number of training samples needed to achieve comparable predictive accuracy. For the RF model, AL required only 710 samples to achieve an R2 score of 0.98, as compared to the 4,785 samples needed by random sampling. Similarly, the FNN model achieved the same R2 score with just 355 samples when using AL, a significant improvement over the 825 samples required by random sampling. In case of uncertainty-based sampling strategy, vFNN attained an R2 of 0.98 with 3,420 samples, reducing the sample requirement by 47% relative to the 6,440 samples needed for random sampling. Its performance suggests that larger training data are required to fully leverage its uncertainty quantification capabilities.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Neural posterior unfolding

Differential cross section measurements are the currency of scientific exchange in particle and nuclear physics. A key challenge for these analyses is the correction for detector distortions, known as deconvolution or unfolding. Binned unfolding of cross section measurements traditionally rely on the regularized inversion of the response matrix that represents the detector response, mapping pre-detector (`particle level') observables to post-detector (`detector level') observables. In this paper we introduce Neural Posterior Unfolding, a modern, Bayesian approach that leverages normalizing flows for unfolding. By using normalizing flows for neural posterior estimation, NPU offers several key advantages including implicit regularization through the neural network architecture, fast amortized inference that eliminates the need for repeated retraining, and direct access to the full uncertainty in the unfolded result. In addition to introducing NPU, we implement a classical Bayesian unfolding method called Fully Bayesian Unfolding (FBU) in modern Python so it can also be studied. These tools are validated on simple Gaussian examples and then tested on simulated jet substructure examples from the Large Hadron Collider (LHC). We find that the Bayesian methods are effective and worth additional development to be analysis ready for cross section measurements at the LHC and beyond.

Analysis and statistical methods↗
DOE OSTI2026

Multi-Modal Bayesian Neural Network Surrogates with Conjugate Last-Layer Estimation

As data collection and simulation capabilities advance, multi-modal learning, the task of learning from multiple modalities and sources of data, is becoming an increasingly important area of research. Surrogate models that learn from data of multiple auxiliary modalities to support the modeling of a highly expensive quantity of interest have the potential to aid outer loop applications such as optimization, inverse problems, or sensitivity analyses when multi-modal data are available. We develop two multi-modal Bayesian neural network surrogate models and leverage conditionally conjugate distributions in the last layer to estimate model parameters using stochastic variational inference (SVI). We provide a method to perform this conjugate SVI estimation in the presence of partially missing observations. Here, we demonstrate improved prediction accuracy and uncertainty quantification compared to unimodal surrogate models for both scalar and time series data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Prime VI

SAND2025-03757O Prime VI is a distribution-of-disease outbreak model calibration code based on variational inference. It accompanies a publication for submission to Statistics in Medicine journal, and the code will be maintained for open-source use on Sandia's GitLab. The software provides methods for calibrating an epidemiological model to measured case-count data for a multitude of correlated spatial regions. The code solves a Bayesian inverse problem for model calibration where the posterior over-model parameters are approximated through a custom implementation of variational inference. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Safta, Cosmin↗
DOE OSTI2026

Bayesian Optimization of Catalysis with In-Context Learning

Large language models (LLMs) can perform accurate classification with zero or few examples through in-context learning (ICL), allowing the model to observe query-relevant examples at inference time and eliminating the need for additional weight updates to generalize beyond its original training data. We extend this capability to regression with uncertainty estimation using frozen LLMs (e.g., GPT-4o, Gemini), enabling Bayesian optimization (BO) in natural language without explicit model training or feature engineering. We apply this to materials discovery by representing materials as synthesis and testing procedures for use in natural language prompts. This Bayesian, design-first approach prioritizes optimization toward target material properties before detailed characterization, in contrast to conventional experimental workflows that often emphasize characterization of suboptimal materials. On benchmarks like aqueous solubility and oxidative coupling of methane (OCM), BO-ICL matches or outperforms Gaussian processes. In live experiments on the reverse water–gas shift (RWGS) reaction, BO-ICL identifies multimetallic catalysts that approach equilibrium CO yield within 6 and 10 iterations from a pool of 3,700 and 360,000 candidates, respectively. Our method redefines materials representation and accelerates discovery, with broad applications across catalysis, materials science, and AI.

Calibration↗
DOE OSTI2025

A novel framework for increasing research transparency: Exploring the connection between diversity and innovation

A split sample/dual method research protocol is demonstrated to increase transparency while reducing the probability of false discovery. We apply the protocol to examine whether diversity in ownership teams increases or decreases the likelihood of a firm reporting a novel innovation using data from the 2018 United States Census Bureau’s Annual Business Survey. Transparency is increased in three ways: 1) all specification testing and identifying potentially productive models is done in an exploratory subsample that 2) preserves the validity of hypothesis test statistics fromde novoestimation in the holdout confirmatory sample with 3) all findings publicly documented in an earlier registered report and in this journal publication. Bayesian estimation procedures that leverage information from the exploratory stage included in the confirmatory stage estimation replace traditional frequentist null hypothesis significance testing. In addition to increasing statistical power by using information from the full sample, Bayesian methods directly estimate a probability distribution for the magnitude of an effect, allowing much richer inference. Estimated magnitudes of diversity along academic discipline, race, ethnicity, and foreign-born status dimensions are positively associated with innovation. A maximally diverse ownership team on these dimensions would be roughly six times more likely to report new-to-market innovation than a homophilic team.

Science & Technology - Other Topics↗
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)↗
DOE OSTI2024

Bayesian mixture model approach to quantifying the empirical nuclear saturation point

The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, $n_0 \approx 0.16 \, \mathrm{fm}^{-3}$, at which the pressure vanishes and the energy per particle attains its minimum, $E_0 \approx -16 \, \mathrm{MeV}$. Although not directly measurable, the nuclear saturation point $(n_0,E_0)$ can be extrapolated by density functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective field theory (EFT). However, when considering several DFT predictions for $(n_0,E_0)$ from Skyrme and Relativistic Mean Field (RMF) models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark nuclear saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $(n_0,E_0)$ using an efficient conjugate prior approach. The inferred posterior distribution for the saturation point's mean and covariance matrix follows a Normal-inverse-Wishart class, resulting in posterior predictives in the form of correlated, bivariate $t$-distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95\% credibility level, we estimate $n_0 \approx 0.157 \pm 0.010 \, \mathrm{fm}^{-3}$ and $E_0 \approx -15.97 \pm 0.40 \, \mathrm{MeV}$ for the marginal (univariate) $t$-distributions. Combined with chiral EFT calculations of the pure neutron matter EOS, we obtain bivariate normal distributions for the nuclear symmetry energy and its slope parameter evaluated at $n_0$: $S_v \approx 32.0 \pm 1.1 \, \mathrm{MeV}$ and $L\approx 52.6\pm 8.1 \, \mathrm{MeV}$ (95\%), respectively. Furthermore, our Bayesian framework is publicly available, so practitioners can readily use and extend our results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Validating sequential Monte Carlo for gravitational-wave inference

Nested sampling (NS) is the preferred stochastic sampling algorithm for gravitational-wave inference for compact binary coalescences. It can handle the complex nature of the gravitational-wave likelihood surface and provides an estimate of the Bayesian model evidence. However, there is another class of algorithms that meets the same requirements, but has not been used for gravitational-wave analyses: sequential Monte Carlo (SMC), an extension of importance sampling that maps samples from an initial density to a target density via a series of intermediate densities. In this work, we validate a type of SMC algorithm, called persistent sampling (PS), for gravitational-wave inference. We consider a range of different scenarios including binary black holes and binary neutron stars and real and simulated data and show that PS produces results that are consistent with NS whilst being, on average, 2 times more efficient and 2.74 times faster. This demonstrates that PS is a viable alternative to NS that should be considered for future gravitational-wave analyses.

black hole mergers↗
DOE OSTI2024

Expanding neutrino oscillation parameter measurements in NOvA using a Bayesian approach

NOvA is a long-baseline neutrino oscillation experiment that measures oscillations in charged-current ν μ → ν μ (disappearance) and ν μ → ν e (appearance) channels, and their antineutrino counterparts, using neutrinos of energies around 2 GeV over a distance of 810 km. In this work we reanalyze the dataset first examined in our previous paper [] using an alternative statistical approach based on Bayesian Markov chain Monte Carlo. We measure oscillation parameters consistent with the previous results. We also extend our inferences to include the first NOvA measurements of the reactor mixing angle θ 13 , where we find 0.071 ≤ sin 2 2 θ 13 ≤ 0.107 , and the Jarlskog invariant, where we observe no significant preference for the C P -conserving value J = 0 over values favoring C P violation. We use these results to examine the effects of constraints from short-baseline measurements of θ 13 using antineutrinos from nuclear reactors when making NOvA measurements of θ 23 . Our long-baseline measurement of θ 13 is shown to be consistent with the reactor measurements, supporting the general applicability and robustness of the Pontecorvo-Maki-Nakagawa-Sakata framework for neutrino oscillations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Inverse prediction of PuO2 processing conditions using Bayesian seemingly unrelated regression with functional data

Over the past decade, a variety of innovative methodologies have been developed to better characterize the relationships between processing conditions and the physical, morphological, and chemical features of special nuclear material (SNM). Different processing conditions generate SNM products with different features, which are known as “signatures” because they are indicative of the processing conditions used to produce the material. These signatures can potentially allow a forensic analyst to determine which processes were used to produce the SNM and make inferences about where the material originated. This article investigates a statistical technique for relating processing conditions to the morphological features of PuO 2 particles. We develop a Bayesian implementation of seemingly unrelated regression (SUR) to inverse-predict unknown PuO 2 processing conditions from known PuO 2 features. Model results from simulated data demonstrate the usefulness of the technique. Applied to empirical data from a bench-scale experiment specifically designed with inverse prediction in mind, our model successfully predicts nitric acid concentration, while results for Pu concentration and precipitation temperature were equivalent to a simple mean model. Our technique compliments other recent methodologies developed for forensic analysis of nuclear material and can be generalized across the field of chemometrics for application to other materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Hayes, Kyle↗
DOE OSTI2025

Correlations between the Neutron Star Mass–Radius Relation and the Equation of State of Dense Matter

We develop an analytic method of inverting the Tolman–Oppenheimer–Volkoff relations to high accuracy. In principle, a specified energy density–pressure relation gives a unique mass–radius (M–R) relation and vice versa. Our method is developed from the strong correlations that are shown to exist between the neutron star mass–radius curve and the equation of state (EOS) or pressure–energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials, and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Rms fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary M–R curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.

Bayesian statistics↗