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DOE OSTI2024

Computing the QRPA level density with the finite amplitude method

Here, we describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Lyapunov-Based Iterative Learning of Regions of Attraction for Autonomous Systems

This paper proposes a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Lyapunov-Based Iterative Learning of the Region of Attraction for Autonomous Systems

This presentation introduces a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗

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 OSTI2025

Online energy consumption forecast for battery electric buses using a learning-free algebraic method

Accurately predicting the energy consumption plays a vital role in battery electric buses (BEBs) route planning and deployment. Based on the algebraic derivative estimation, we present a novel method to forecast the energy consumption in real time. In contrast to the mainstream machine-learning-based methods, the proposed method does not require access to the historical energy consumption data. It eliminates the time-consuming and computationally expensive offline training. Consequently, its prediction performance is not constrained by the quantity and quality of the training data. Moreover, the method can swiftly adapt to new situations not included in the previous driving cycles, which makes it especially suitable for emerging transport modes, e.g., on-demand transit services. In addition, its online execution only involves algebraic calculations, yielding superior calculation efficiency. Using real-world data, we comprehensively compare the performance of the proposed learning-free algebraic method with multiple representative machine-learning-based methods. Finally, the advantages and limitations of the proposed method are discussed in detail.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

Diesel Fuel Consumption in Prominent U.S. Open-Pit Mines: Site-Level Estimates

This report presents a comprehensive framework for estimating diesel fuel consumption and prices at open-pit mines in the United States. The framework includes transparent methods for calculating site-level diesel energy use when direct reporting is unavailable, and a structured confidence evaluation for each method. The framework is demonstrated to estimate current diesel consumption at 21 open-pit mines in the United States. Initial findings support ongoing efforts to strengthen the competitiveness and security of the U.S. industrial base by supporting data-driven supply chain analysis and decision-making, improved transparency in mining sector energy use, and targeted deployment of energy innovation and cost-reduction strategies. Future updates to the dataset—coupled with expanded data transparency and method validation—will help ensure that the findings remain relevant as the sector continues to evolve.

02 PETROLEUM↗

DOE OSTI2025

Advances in geophysical forensic event monitoring

Forensic analysis of man-made, non-nuclear events (such as industrial accidents, explosion experiments and mine collapses) has become more frequent and detailed owing to advancements in geophysical monitoring. Here, in this Technical Review, we demonstrate how geophysical forensic monitoring using seismic, infrasound and hydroacoustic recordings provides insights on events in the solid earth, atmosphere and underwater. Advanced techniques, including machine-learning-based models, have been developed to detect, identify and investigate these events, providing information on location, subevents, sources and explosive yield. The increase in data availability, application of advanced methods and computation and the growth of multitechnology approaches have increased the accuracy of forensic event analysis and enabled more realistic characterization of uncertainties. For example, the 2020 Beirut explosion in Lebanon demonstrated that various seismic, acoustic and other methods could be used to estimate explosive yield (and yield uncertainties) of about 1 ktonne, providing confidence in the application of these methods to smaller events where data are available. However, forensic investigations remain largely limited to known events with identified sources. Increased access to data, sophisticated analysis methods and high-resolution earth models will improve forensic event analysis further, enabling civil and scientific applications, such as localization in the search for the lost ARA San Juan submarine.

geophysics↗

DOE OSTI2024

An Approach to Dynamic Human Reliability Analysis and Its Data Collection Framework

Human reliability analysis (HRA) is a method for evaluating human errors in a variety of complex systems such as nuclear power plants, military systems, aircraft, and chemical plants. Most HRA methods currently used by regulatory institutes or utilities are called static HRA and are carried out by simple worksheets or simple calculators. To date, there are many unsolved or intrinsic challenges in static HRA. For example, existing static HRA does not realistically model and evaluate human actions as they would be performed at actual systems. There is no method with HRA to objectively estimate the time required for human actions despite being essential to HRA processes. In addition, many HRA methods still rely on a dataset generated prior to the 1980s, from unrelated industry experience or simply from expert judgment. Accordingly, this study attempted to research how to overcome the challenges of existing HRA via dynamic risk assessment (a.k.a., simulation-based or computation-based risk assessment) techniques. First, this study developed a dynamic HRA method, named as PRocedure-based Investigation Method of EMRALD Risk Assessment – HRA (PRIMERA-HRA). The PRIMERA-HRA mainly concentrates on providing HRA analysts with specific guidelines on how to reasonably model human actions, assign human reliability data and evaluate output of simulation within a dynamic probabilistic risk assessment tool, called as Event Modeling Risk Assessment using Linked Diagrams (EMRALD). Second, this study also developed a module for performance shaping factors (i.e., the key concept in HRA quantification) applicable to dynamic HRA, then implemented it based on PRIMERA-HRA within the EMRALD tool. Third, this study developed an HRA data collection framework to support dynamic HRA, called as Simplified Human Error Experimental Program (SHEEP). Originally, the SHEEP study aimed to support static HRA and its data collection, but recently extended the scope to the new technologies such as dynamic HRA or HRA for advanced reactors. SHEEP focuses on the use of data collected from simplified simulators to complement—but not replace—data collection studies using full-scope simulators and actual operators. To date, many experiments were conducted under the SHEEP framework. Multiple analyses, such as human performance analysis, human error analysis, task complexity analysis, learning effect analysis and time distribution analysis, were also carried out using the collected data. Then, based on the major insights, an approach to inferring full-scope data based on simplified simulator data was proposed. The PRIMERA-HRA and SHEEP research are expected to evaluate human actions more realistically than existing static HRA, provide an opportunity to collect more HRA data with reasonable cost and labor, then contribute to enhance the quality of HRA.

99 - GENERAL AND MISCELLANEOUS↗

DOE OSTI2024

Effect of Sample Thickness on the Tensile Strength of Small Graphite Discs

This report formally documents the completion of the Advanced Reactor Technologies (ART) Level 3 Milestone (M3TG-24OR0501054), “Continue activities related to Split Disc-DIC - complete analysis of effect of sample thickness on one fine grain graphite,” due May 31, 2024. Details within this report outline the status of activities aimed at elucidating the effect of sample thickness on the tensile strength measurement using the small-disc, split-disc testing standard in support of the US Department of Energy’s ART Graphite R&D Program. The ASTM D8289, Standard Test Method for Tensile Strength Estimate by Disc Compression of Manufactured Graphite, was developed to provide an alternative means for testing tensile strength on smaller specimens, which are compatible with available irradiation capsule volumes, and other compatibility measurements. ASTM D8289 specifies that acceptable specimen diameter can range from 6 to 12.7 mm and that the maximum allowed sample thickness should be half of the diameter. However, information is limited with respect to the effect of thickness on the measured splitting tensile strength. This report documents efforts to understand the effect of sample thickness on splitting tensile strength. The work involved testing Ø12.7 mm samples of fine-grain graphites 2114 and IG-110 of different thicknesses (6.35, 5, 4, and 3 mm). The digital image correlation (DIC) method was applied to the samples, along with the ASTM D8289 Standard, to help interpret the measured results.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

36 MATERIALS SCIENCE↗

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

Transmission Interface Limits for High-Spatial Resolution Capacity Expansion Modeling

Large-scale capacity expansion models typically rely on estimates of the power transfer limits between modeled zones. Accurate estimation of these interface transfer limits (ITLs) requires modeling the underlying transmission network. Here we expand on a maximum flow optimization method that uses linearized power flow to estimate transfer limits. We apply this method to a data set of the U.S. transmission network to estimate ITLs between U.S. counties. By calculating ITLs using different subsets of the network, we evaluate how the size of the network used in the estimation affects the results. The results show diminishing returns to ITL accuracy after six hops, suggesting that a network subset can reasonably be used to approximate ITLs. The county-level estimates produced in this study will support more spatially resolved capacity expansion modeling and will help inform policy making at local and national levels.

capacity planning↗

DOE OSTI2024

Transmission Interface Limits for High-Spatial Resolution Capacity Expansion Modeling

capacity planning↗

DOE OSTI2025

Quantifying Groundwater Response and Uncertainty in Beaver‐Influenced Mountainous Floodplains Using Machine Learning‐Based Model Calibration

Abstract Beavers ( Castor canadensis ) alter river corridor hydrology by creating ponds and inundating floodplains, and thereby improving surface water storage. However, the impact of inundation on groundwater, particularly in mountainous alluvial floodplains with permeable gravel/cobble layers overlain by a soil layer, remains uncertain. Numerical modeling across various floodplain structures considers topographic and sediment complexity and multidirectional flow, linking inundation to groundwater response. This study develops a model‐data integration workflow to address uncertainty in groundwater response to beaver‐induced inundations in a mountainous alluvial floodplain in the Upper Colorado River Basin. Uncertain factors include seasonal hydrologic dynamics, hydraulic conductivities, floodplain structures, and meteorological forcings. We employed an ensemble of groundwater models, based on geophysical and hydrologic data, with machine learning‐based calibration using a neural density estimator. This allowed us to quantify the vertical flux from the soil layer to the permeable gravel bed, the down‐valley underflow within the gravel bed, and their ratios. Results show a significant increase in the vertical flux relative to down‐valley underflow, from 2 during dry pond periods to 20 during wet periods, serving as an analogy for conditions without and with beaver ponds. The study highlights the influence of floodplain structure on groundwater storage, water balance, and water quality impacted by beaver ponds. A thick gravel bed layer, with a large down‐valley underflow, minimizes the effect of beaver‐induced inundation on water quality. We emphasize the need for field‐scale measurements of floodplain structure and improved characterization of evapotranspiration changes to reduce uncertainty in groundwater response. Plain Language Summary Beavers change the flow of water in river corridors by creating ponds, expanding wetlands, and flooding floodplains. This increases surface water area, promotes plant growth, and enhances biodiversity. However, the impact of this flooding on groundwater flow is not well understood, especially in mountainous areas with gravel layers where water moves easily beneath soil. In this study, we used numerical modeling to investigate how beaver ponds influence groundwater in a mountainous floodplain of the Upper Colorado River Basin. We adapted a machine learning method to validate our numerical models using multiple field data sets. Our findings show that beaver ponds significantly increase vertical water flow from the soil to the gravel during wet periods, compared to when the ponds are fully drained. The study also highlights the importance of floodplain structure in controlling both water flow in gravel layers along the river direction and vertical flow from the soil to the gravel with the presence of beavers. To reduce uncertainty in groundwater response, we emphasize the need for more field‐scale measurements of floodplain structure, hydraulic properties, and evapotranspiration changes. Key Points Floodplain structures and hydraulic conductivities are important for groundwater response with beaver ponds in mountainous floodplains Large down‐valley underflow in permeability‐stratified floodplains reduces beaver‐induced impacts on groundwater storage and water quality Machine learning‐based model calibration methods are effective for estimating posterior distributions of groundwater model parameters

Wang, Lijing↗

DOE OSTI2024

Managing negative values is reservoir inflow computation: A case study

Reservoir inflow is conventionally estimated using the water balance method, which involves the reservoir release and the change in storage during the period considered. As a result, the estimated inflow may sometimes be negative as the errors involved in each input variable build-up to the output. In our study, the fleet data was provided by the Tennessee Valley Authority (TVA) for their Norris Hydropower facility. Unlike the flow release data, which was readily accessible, the change in storage had to be calculated using the reservoir elevation and volume relationship. The original inflow estimates produced a wide range of negative values with large outliers, making it difficult to visualize the current trends. This paper describes a methodology to remove the negative values encountered during the inflow computation, and the results were analyzed by correlating with the nearby streamflow gaging stations.

Shibu, Asha↗

DOE OSTI2025

Hierarchical Speed Planner for Automated Vehicles: A Framework for Lagrangian Variable Speed Limit in Mixed-Autonomy Traffic

Here, this article presents a novel hierarchical speed planning framework for variable speed limits in mixed-autonomy traffic environments, leveraging server-side macroscopic control and vehicle-side microscopic execution. The framework integrates real-time traffic state estimation (TSE) and reinforcement learning (RL)-based control to mitigate congestion and improve traffic flow. A TSE enhancement module combines macroscopic data from sources like INRIX with high-resolution observations from connected autonomous vehicles (CAVs), enabling predictive modeling to address latency and noise. The target speed design module employs kernel smoothing and a buffer zone strategy to optimize traffic density and flow around bottlenecks. The proposed system was validated in the largest open-road test to date with 100 CAVs, demonstrating an overall 8% traffic density decrease, with a specific decrease of 7% upstream, 10% downstream, and a 52% decrease during the congestion formation phase at bottlenecks.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Standardising the “Gregory method” for calculating equilibrium climate sensitivity

The equilibrium climate sensitivity (ECS) – the equilibrium global mean temperature response to a doubling of atmospheric CO 2 – is a high-profile metric for quantifying the Earth system's response to human-induced climate change. A widely applied approach to estimating the ECS is the “Gregory method” (Gregory et al., 2004), which uses an ordinary least squares (OLS) regression between the net radiative flux, N, and surface air temperature anomalies, ΔT, from a 150 year experiment in which atmospheric CO 2 concentrations are quadrupled. The ECS is determined by extrapolating the linear fit to N=0, i.e. the ΔT-intercept, indicating the point at which the system is back in equilibrium. This method has been used to compare ECS estimates across the CMIP5 and CMIP6 ensembles and will likely be a key diagnostic for CMIP7. Despite its widespread application, there is little consistency or transparency between studies in how the climate model data is processed prior to the regression, leading to potential discrepancies in ECS estimates. We identify 32 alternative data processing pathways, varying by differences in global mean weighting, net radiative flux variable, anomaly calculation method, and linear regression fit. Using 44 CMIP6 models, we systematically assess the impact of these choices on ECS estimates and calculate uncertainty ranges using two bootstrap approaches. While the inter-model ECS range is insensitive to the data processing pathway, individual outlier models exhibit notable differences. Approximating a model's native grid cell area (if irregular) with cosine of the latitude can decrease the ECS by 11 %, the choice of N-variable can change the ECS by 6 %, and some anomaly calculation methods can introduce spurious temporal correlations in the processed data. Beyond data processing choices, we also evaluate an alternative linear regression method – total least squares (TLS) – which has a more statistically robust basis than OLS. However, for consistency with previous literature, and given TLS may reduce the ECS compared to OLS (by up to 24 %), thereby making a known bias in the Gregory method worse, we do not feel there is sufficient clarity to recommend a transition to TLS in all cases. To improve reproducibility and comparability in future studies, we recommend a standardised Gregory method: weighting the global mean by cell area, using the top of the atmosphere (as opposed to the top of model) N-variable, and calculating anomalies by first applying a rolling average to the preindustrial control timeseries then subtracting from the raw CO 2 quadrupling experiment. This approach accounts for model drift while reducing noise in the data to best meet the pre-conditions of the linear regression. While CMIP6 results of the multi-model mean ECS appear insensitive to these processing choices, similar assumptions may not hold for CMIP7, underscoring the need for standardised data preparation in future climate sensitivity assessments.

Geosciences↗

DOE OSTI2025

Overview of the SCEC/USGS Community Stress Drop Validation Study Using the 2019 Ridgecrest Earthquake Sequence

We present initial findings from the ongoing Community Stress Drop Validation Study to compare spectral stress-drop estimates for earthquakes in the 2019 Ridgecrest, California, sequence. This study uses a unified dataset to independently estimate earthquake source parameters through various methods. Stress drop, which denotes the change in average shear stress along a fault during earthquake rupture, is a critical parameter in earthquake science, impacting ground motion, rupture simulation, and source physics. Spectral stress drop is commonly derived by fitting the amplitude-spectrum shape, but estimates can vary substantially across studies for individual earthquakes. Sponsored jointly by the U.S. Geological Survey and the Statewide (previously, Southern) California Earthquake Center our community study aims to elucidate sources of variability and uncertainty in earthquake spectral stress-drop estimates through quantitative comparison of submitted results from independent analyses. The dataset includes nearly 13,000 earthquakes ranging from M 1 to 7 during a two-week period of the 2019 Ridgecrest sequence, recorded within a 1° radius. Here, in this article, we report on 56 unique submissions received from 20 different groups, detailing spectral corner frequencies (or source durations), moment magnitudes, and estimated spectral stress drops. Methods employed encompass spectral ratio analysis, spectral decomposition and inversion, finite-fault modeling, ground-motion-based approaches, and combined methods. Initial analysis reveals significant scatter across submitted spectral stress drops spanning over six orders of magnitude. However, we can identify between-method trends and offsets within the data to mitigate this variability. Averaging submissions for a prioritized subset of 56 events shows reduced variability of spectral stress drop, indicating overall consistency in recovered spectral stress-drop values.

58 GEOSCIENCES↗