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DOE OSTI2024

a priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks

While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulations (DNS) create opportunities to leverage data-driven modeling techniques. Albeit flexible, data-driven models still depend on the dataset and the functional form of the model chosen. Increased adoption of such models requires reliable uncertainty estimates both in the data-informed and out-of-distribution regimes. Here, in this work, we employ Bayesian neural networks (BNNs) to capture both epistemic and aleatoric uncertainties in a reacting flow model. In particular, we model the filtered progress variable scalar dissipation rate which plays a key role in the dynamics of turbulent premixed flames. We demonstrate that BNN models can provide unique insights about the structure of uncertainty of the data-driven closure models. We also propose a method for the incorporation of out-of-distribution information in a BNN, which can be used for out-of-distribution query detection. The efficacy of the model is demonstrated by a priori evaluation on a dataset consisting of a variety of flame conditions and fuels.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A comparison of Gaussian processes and neural networks for computer model emulation and calibration

The Department of Energy relies on complex physics simulations for prediction in domains like cosmology, nuclear theory, and materials science. These simulations are often extremely computationally intensive, with some requiring days or weeks for a single simulation. In order to assure their accuracy, these models are calibrated against observational data in order to estimate inputs and systematic biases. Because of their great computational complexity, this process typically requires the construction of an emulator, a fast approximation to the simulation. In this paper, two emulator approaches are compared: Gaussian process regression and neural networks. Their emulation accuracy and calibration performance on three real problems of Department of Energy interest is considered. On these problems, the Gaussian process emulator tends to be more accurate with narrower, but still well-calibrated uncertainty estimates. The neural network emulator is accurate, but tends to have large uncertainty on its predictions. Finally, as a result, calibration with the Gaussian process emulator produces more constrained posteriors that still perform well in prediction.

97 MATHEMATICS AND COMPUTING↗

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 OSTI2022

Improved indirect limits on charm and bottom quark EDMs

We derive indirect limits on the charm and bottom quark electric dipole moments (EDMs) from paramagnetic AMO and neutron EDM experiments. The charm and bottom quark EDMs generate CP-odd photon-gluon operators and light quark EDMs at the c- and b-quark mass thresholds. These CP-odd operators induce the CP-odd semi-leptonic operator C S and the neutron EDM below the QCD scale that are probed by the paramagnetic and neutron EDM experiments, respectively. The bound from C S is |d c | < 1.3 × 10 –20 e cm for the charm quark and |d b | < 7.6 × 10 –19 e cm for the bottom quark, with its uncertainty estimated as 10 %. The neutron EDM provides a stronger bound, |d c | < 6 × 10 –22 e cm and |d b | < 2 × 10 –20 e cm, though with a larger hadronic uncertainty.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗

DOE OSTI2021

Droplet Number Concentration Value-Added Product

The ndrop_mfrsr value-added product (VAP) provides an estimate of the cloud droplet number concentration of overcast water clouds retrieved from cloud optical depth from the multi-filter rotating shadowband radiometer (MFRSR) instrument and liquid water path (LWP) retrieved from the microwave radiometer (MWR). When cloud layer information is available from vertically pointing lidar and radars in the Active Remote Sensing of Clouds (ARSCL) product, the VAP also provides estimates of the adiabatic LWP and an adiabatic parameter (beta) that indicates how divergent the LWP is from the adiabatic case. quality control (QC) flags (qc_drop_number_conc), an uncertainty estimate (drop_number_conc_toterr), and a cloud layer type flag (cloud_base_type) are useful indicators of the quality and accuracy of any given value of the retrieval. Examples of these major input and output variables are given in sample plots in section 6.0.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

NuSTAR Survey of Obscured Swift/BAT-selected Active Galactic Nuclei. II. Median High-energy Cutoff in Seyfert II Hard X-Ray Spectra

Broadband X-ray spectroscopy of the X-ray emission produced in the coronae of active galactic nuclei (AGNs) can provide important insights into the physical conditions very close to their central supermassive black holes. The temperature of the Comptonizing plasma that forms the corona is manifested through a high-energy cutoff that has been difficult to directly constrain even in the brightest AGN because it requires high-quality data at energies above 10 keV. In this paper we present a large collection of coronal cutoff constraints for obscured AGNs based on a sample of 130 AGNs selected in the hard X-ray band with Swift/BAT and observed nearly simultaneously with NuSTAR and Swift/XRT. Additionally, we find that under a reasonable set of assumptions regarding partial constraints the median cutoff is well constrained to 290 ± 20 keV, where the uncertainty is statistical and given at the 68% confidence level. We investigate the sensitivity of this result to our assumptions and find that consideration of various known systematic uncertainties robustly places the median cutoff between 240 and 340 keV. The central 68% of the intrinsic cutoff distribution is found to be between about 140 and 500 keV, with estimated uncertainties of 20 and 100 keV, respectively. In comparison with the literature, we find no clear evidence that the cutoffs in obscured and unobscured AGNs are substantially different. Our analysis highlights the importance of carefully considering partial and potentially degenerate constraints on the coronal high-energy cutoff in AGNs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Reconstruction and uncertainty quantification of lattice Hamiltonian model parameters from observations of microscopic degrees of freedom

The emergence of scanning probe and electron beam imaging techniques has allowed quantitative studies of atomic structure and minute details of electronic and vibrational structure on the level of individual atomic units. These microscopic descriptors, in turn, can be associated with local symmetry breaking phenomena, representing the stochastic manifestation of the underpinning generative physical model. In this work, we explore the reconstruction of exchange integrals in the Hamiltonian for a lattice model with two competing interactions from observations of microscopic degrees of freedom and establish the uncertainties and reliability of such analysis in a broad parameter-temperature space. In contrast to other approaches, we specifically specify a loss function inherent to thermodynamic systems and utilize it to estimate uncertainty in simulated realizations of different models. As an ancillary task, we develop a machine learning approach based on histogram clustering to predict phase diagrams efficiently using a reduced descriptor space. We further demonstrate that reconstruction is possible well above the phase transition and in the regions of parameter space when the macroscopic ground state of the system is poorly defined due to frustrated interactions. This suggests that this approach can be applied to the traditionally complex problems of condensed matter physics such as ferroelectric relaxors and morphotropic phase boundary systems, spin and cluster glasses, and quantum systems once the local descriptors linked to the relevant physical behaviors are known.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Pooling Data Improves Multimodel IDF Estimates over Median-Based IDF Estimates: Analysis over the Susquehanna and Florida

Traditional multimodel methods for estimating future changes in precipitation intensity, duration, and frequency (IDF) curves rely on mean or median of models’ IDF estimates. Such multimodel estimates are impaired by large estimation uncertainty, shadowing their efficacy in planning efforts. Here, assuming that each climate model is one representation of the underlying data generating process, i.e., the Earth system, we propose a novel extension of current methods through pooling model data: (i) evaluate performance of climate models in simulating the spatial and temporal variability of the observed annual maximum precipitation (AMP), (ii) bias-correct and pool historical and future AMP data of reasonably performing models, and (iii) compute IDF estimates in a nonstationary framework from pooled historical and future model data. Pooling enhances fitting of the extreme value distribution to the data and assumes that data from reasonably performing models represent samples from the “true” underlying data generating distribution. Through Monte Carlo simulations with synthetic data, we show that return periods derived from pooled data have smaller biases and lesser uncertainty than those derived from ensembles of individual model data. We apply this method to NA-CORDEX models to estimate changes in 24-h precipitation intensity–frequency (PIF) estimates over the Susquehanna watershed and Florida peninsula. Our approach identifies significant future changes at more stations compared to median-based PIF estimates. The analysis suggests that almost all stations over the Susquehanna and at least two-thirds of the stations over the Florida peninsula will observe significant increases in 24-h precipitation for 2–100-yr return periods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗

DOE OSTI2022

SCALE 6.2.4 Validation: Radiation Shielding

For safe and reliable use of computer codes by the community, accuracy must be clearly evaluated. In particular, the nuclear reactor engineering and licensing field needs accurate tools for radiation shielding modeling. Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC) is one such tool, with built-in variance reduction methods distributed within the SCALE code, and its validity is demonstrated in this report for the released version 6.2.4. Representative benchmarks corresponding to shielding analysis are selected for the validation study. Typical experimental results analyzed from those benchmarks include neutron fluxes, detector count rates, detector energy response functions, neutron and gamma doses, foil neutron activation rates and activities, neutron leakage fluxes, and skyshine dose rates. Thousands of points of comparison between experiment and calculation are presented in this work. Other than rare outliers typically explained by either a lack of information or large uncertainties in the experiment conditions, material, or dimensions, MAVRIC agrees well with the experiment results. MAVRIC is also compared to Monte Carlo N-Particle (MCNP) calculations when available, and both codes generally produce good agreements within estimated uncertainties. The selected benchmarks are obtained from reliable sources such as the International Criticality Safety Benchmark Evaluation Project Handbook (ICSBEP Handbook), the Shielding Integral Benchmark Archive & Database (SINBAD), and other shielding validation work found in the literature. Additional datapoints and benchmarks will be added to future versions of this report to incrementally expand the shielding validation suite incrementally.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2022

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Evaluating Probabilistic Deep Learning Methods for Uncertainty Quantification of Precipitation Bias Correction

Climate models often exhibit biases in their precipitation predictions, particularly underestimating high-intensity events and overestimating low precipitation. Deep learning approaches offer promising solutions, but their epistemic uncertainty associated with a deep learning–based bias correction method has not previously been quantified for reliable downstream climate impact studies. While methods for capturing the epistemic uncertainty in deep learning frameworks exist, there is currently no consensus on the best method. In this work, we compare three uncertainty quantification (UQ) methods—Deep Ensembles (DEns), Monte Carlo Dropout (MCD), and Flipout—by assessing the reliability of their uncertainty estimates using standard measures such as sharpness and calibration. These UQ methods are applied to an existing deep learning precipitation bias correction model known as UFNet: a coupled U-Net and fully connected neural network. The methods utilized to assess the models’ uncertainties are 1) calibration, which ensures that the expected probabilities of the model align with reality and 2) sharpness, which is a measure of the precision of the model’s probabilistic predictions. Of the three UQ methods evaluated, the DEns and MCD methods demonstrated the best-calibrated performance (expected calibration error of 0.36 and 0.35, respectively), compared to Flipout (0.58). In contrast, Flipout had the sharpest predictions and the highest metric performance in bias correcting precipitation—especially for higher-order moments such as kurtosis with a spatial correlation of 72% compared to 32% and 55% spatial correlation for DEns and MCD, respectively. Of the three UQ methods, MCD was found to be the most suitable method for UQ purposes based on its calibration, sharpness, and computational requirements.

Bayesian methods↗

DOE OSTI2023

Tidal Turbine Benchmarking Project: Stage I - Steady Flow Blind Predictions: Preprint

This paper presents the first blind prediction stage of the Tidal Turbine Benchmarking Project being conducted and funded by the UK's EPSRC and Supergen ORE Hub. In this first stage, only steady flow conditions, at low and elevated turbulence (3.1%) levels, were considered. Prior to the blind prediction stage, a large laboratory scale experiment was conducted in which a highly instrumented 1.6m diameter tidal rotor was towed through a large towing tank in well-defined flow conditions with and without an upstream turbulence grid. Details of the test campaign and rotor design were released as part of this community blind prediction exercise. Participants were invited to use a range of engineering modelling approaches to simulate the performance and loads of the turbine. 26 submissions were received from 12 groups from across academia and industry using solution techniques ranging from blade resolved computational fluid dynamics through actuator line, boundary integral element methods, vortex methods to engineering Blade Element Momentum methods. The comparisons between experiments and blind predictions were extremely positive helping to provide validation and uncertainty estimates for the models, but also validating the experimental tests themselves. The exercise demonstrated that the experimental turbine data provides a robust data set against which researchers and design engineers can test their models and implementations to ensure robustness in their processes, helping to reduce uncertainty and provide increased confidence in engineering processes. Furthermore, the data set provides the basis by which modellers can evaluate and refine approaches.

benchmarking↗

DOE OSTI2021

A New Approach to Evaluate and Reduce Uncertainty of Model-Based Biodiversity Projections for Conservation Policy Formulation

Biodiversity projections with uncertainty estimates under different climate, land-use, and policy scenarios are essential to setting and achieving international targets to mitigate biodiversity loss. Evaluating and improving biodiversity predictions to better inform policy decisions remains a central conservation goal and challenge. A comprehensive strategy to evaluate and reduce uncertainty of model outputs against observed measurements and multiple models would help to produce more robust biodiversity predictions. We propose an approach that integrates biodiversity models and emerging remote sensing and in-situ data streams to evaluate and reduce uncertainty with the goal of improving policy-relevant biodiversity predictions. In this work, we describe a multivariate approach to directly and indirectly evaluate and constrain model uncertainty, demonstrate a proof of concept of this approach, embed the concept within the broader context of model evaluation and scenario analysis for conservation policy, and highlight lessons from other modeling communities.

essential biodiversity variables↗

DOE OSTI2022

Uncertainty Aware Deep Learning for Particle Accelerators

Standard deep learning models for classification and regression applications are ideal for capturing complex system dynamics. However, their predictions can be arbitrarily inaccurate when the input samples are not similar to the training data. Implementation of distance aware uncertainty estimation can be used to detect these scenarios and provide a level of confidence associated with their predictions. In this paper, we present results from using Deep Gaussian Process Approximation (DGPA) methods for errant beam prediction at Spallation Neutron Source (SNS) accelerator (classification) and we provide an uncertainty aware surrogate model for the Fermi National Accelerator Lab (FNAL) Booster Accelerator Complex (regression).

Rajput, Kishansingh↗

DOE OSTI2026

WINDPROF: Merged Best-Estimate Wind Profile Data – Site A1 (AWAKEN Campaign)

WINDPROF provides 10-minute wind and turbulence profiles, integrating Doppler lidars and anemometers during the AWAKEN campaign. Key data include wind speed, direction, vertical velocity, and turbulence parameters, with standardized quality control (e.g., instrument-specific thresholds and inter-instrument validation). Profiles are interpolated to a height grid (20 m spacing below 100 m; 30 m above) and include uncertainty estimates, offering reproducible methods for atmospheric research, model validation, and wind energy studies.

17 WIND ENERGY↗

DOE OSTI2026

WINDPROF: Merged Best-Estimate Wind Profile Data – Site A2 (AWAKEN Campaign)

17 WIND ENERGY↗