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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 OSTI2024

Probabilistic Analysis of Uncertainty in ATRC Flux Profiles

ATRC is a replica of the larger ATR design and is used to conduct research and obtain data such as flux measurements, excess reactivity, and loading requirements before being loaded into ATR. One method for determining the impact an experiment will have at ATR is by looking at the axial flux profile along the fuel rod in the corresponding ATRC experiment; however, flux wand measurements includes large amounts of variation which makes drawing conclusions from the data difficult. This poster describes a definitive method to propagate the uncertainty from ATRC measurements using Python code.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Physics-Informed Sparse Gaussian Process for Probabilistic Stability Analysis of Large-Scale Power System with Dynamic PVs and Loads

This work proposes a physics-informed sparse Gaussian process (SGP) for probabilistic stability assessment of large-scale power systems in the presence of uncertain dynamic PVs and loads. The differential and algebraic equations considering uncertainties from dynamic PVs and loads are reformulated to a nonlinear mapping relationship that allows the application of SGP. Thanks to the nonparametric characteristic of Gaussian process, the proposed framework does not require distributions of uncertain inputs and this distinguishes it from existing approaches. As the original Gaussian process is not scalable to large-scale systems with high dimensional uncertain inputs, this paper develops the SGP with a stochastic variational inference technique. It leads to approximately two orders of complex reduction. A data pre-processing step is also introduced to tackle the coexistence of stable and unstable cases by sample clustering and constructing separate SGPs. The probabilistic transient stability index is analyzed to assess system stability under different uncertain dynamics loads and PVs. Comparisons are performed with the sampling-based, the polynomial chaos expansion-based, and traditional Gaussian process-based methods on the modified IEEE 118-bus and Texas 2000-bus systems under various scenarios, including different levels of uncertainties and the existence of nonlinear correlations among dynamic PVs. The impacts of data quality and quantity issues are also investigated. It is shown that the proposed SGP achieves significantly improved computational efficiency while maintaining high accuracy with a limited number of data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Density of states prediction for materials discovery via contrastive learning from probabilistic embeddings

Abstract Machine learning for materials discovery has largely focused on predicting an individual scalar rather than multiple related properties, where spectral properties are an important example. Fundamental spectral properties include the phonon density of states (phDOS) and the electronic density of states (eDOS), which individually or collectively are the origins of a breadth of materials observables and functions. Building upon the success of graph attention networks for encoding crystalline materials, we introduce a probabilistic embedding generator specifically tailored to the prediction of spectral properties. Coupled with supervised contrastive learning, our materials-to-spectrum (Mat2Spec) model outperforms state-of-the-art methods for predicting ab initio phDOS and eDOS for crystalline materials. We demonstrate Mat2Spec’s ability to identify eDOS gaps below the Fermi energy, validating predictions with ab initio calculations and thereby discovering candidate thermoelectrics and transparent conductors. Mat2Spec is an exemplar framework for predicting spectral properties of materials via strategically incorporated machine learning techniques.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Motion Planning Algorithms for Safety and Quantum Computing Efficiency

Motion planning remains a fundamental problem in robotics. Sampling-based algorithms use randomization to allow efficient solutions to this complex problem. As mobile robots and autonomous vehicles become more prevalent in everyday life, motion planning must be applied to increasingly challenging scenarios. Safety has become a paramount concern in motion planning for ensuring robotic applications enrich human lives. To date, many motion planning techniques to increase safety in the face of uncertain and dynamic environments have been developed. This dissertation first addresses distributional safety of Rapidly-Exploring Random Trees (RRT) through our algorithm W-Safe RRT. To acknowledge distributional uncertainty and poor modeling, W-Safe RRT uses the Wasserstein metric to provide a probabilistic bound on the distributional distance between a robot and obstacles. Human-interpretable environmental agent classification allows online safety margin adaptation. We propose and analyze an integrating region method for online classification that increases actor labeling accuracy based on behavioral feature values when compared to state of the art methods. The method performs class assignments based on local maximum likelihood in a created behavioral feature-space, allowing a notion of classification uncertainty. Model-based methods with safety guarantees can quickly become computationally in tractable, especially with multiple agents, higher dimensions, and plentiful unknowns. Sampling based algorithms have been parallelized for computation with multi-core computers and GPUs. We consider the use of quantum algorithms and computers for sampling-based motion planning for the first time. Quantum computing performs operations on superpositions of states and can solve certain problems much more efficiently than classical computers, but introduces previously unseen challenges. With Quantum-RRT, we recast the motion planning problem into a database-search structure and use Quantum Amplitude Amplification to find reachable states in the database with a quadratic performance increase over classical methods. We address two error sources with this method: quantum measurement and quantum oracle errors. We then extend this method to Parallel Quantum-RRT, which uses a manager-worker architecture with multiple parallel quantum workers to increase database search efficiency. We compare algorithm architectures and characterize probabilities of multiple workers finding solutions. Lastly, we test in simulation the quantum algorithms against classical versions in a wide variety of scenarios, concluding that a similar parallelization improvement is to be found in the quantum case as was found in the parallelization of classical RRT.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1983

Statistical Analysis of a Debugging Model

Suppose that a system is undergoing a sequence of trials and design changes in an effort to find and eliminate design flaws in the system. Specifically, suppose that each trial is classified as an assignable cause failure (if the failure is due to one or more design flaws), an inherent failure (if the failure is not due to a design flaw), or a success. After each assignable cause failure, the design flaws that caused the failure are removed. In the case of statistically independent and identical design flaws, a probabilistic model is developed to describe this debugging process. Explicit expressions are obtained for the distributions of the important random variables and for the important measures of reliability. Statistical methods are developed for estimating the parameters of the model from accumulated test data.

Siegrist, K.↗

NASA NTRS1999

Unifying Model-Based and Reactive Programming within a Model-Based Executive

Real-time, model-based, deduction has recently emerged as a vital component in AI's tool box for developing highly autonomous reactive systems. Yet one of the current hurdles towards developing model-based reactive systems is the number of methods simultaneously employed, and their corresponding melange of programming and modeling languages. This paper offers an important step towards unification. We introduce RMPL, a rich modeling language that combines probabilistic, constraint-based modeling with reactive programming constructs, while offering a simple semantics in terms of hidden state Markov processes. We introduce probabilistic, hierarchical constraint automata (PHCA), which allow Markov processes to be expressed in a compact representation that preserves the modularity of RMPL programs. Finally, a model-based executive, called Reactive Burton is described that exploits this compact encoding to perform efficIent simulation, belief state update and control sequence generation.

Williams, Brian C.↗

NASA NTRS2003

CARES/LIFE Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program

This manual describes the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction (CARES/LIFE) computer program. The program calculates the time-dependent reliability of monolithic ceramic components subjected to thermomechanical and/or proof test loading. CARES/LIFE is an extension of the CARES (Ceramic Analysis and Reliability Evaluation of Structures) computer program. The program uses results from MSC/NASTRAN, ABAQUS, and ANSYS finite element analysis programs to evaluate component reliability due to inherent surface and/or volume type flaws. CARES/LIFE accounts for the phenomenon of subcritical crack growth (SCG) by utilizing the power law, Paris law, or Walker law. The two-parameter Weibull cumulative distribution function is used to characterize the variation in component strength. The effects of multiaxial stresses are modeled by using either the principle of independent action (PIA), the Weibull normal stress averaging method (NSA), or the Batdorf theory. Inert strength and fatigue parameters are estimated from rupture strength data of naturally flawed specimens loaded in static, dynamic, or cyclic fatigue. The probabilistic time-dependent theories used in CARES/LIFE, along with the input and output for CARES/LIFE, are described. Example problems to demonstrate various features of the program are also included.

Nemeth, Noel N.↗

NASA NTRS2005

Gesture Based Control and EMG Decomposition

This paper presents two probabilistic developments for use with Electromyograms (EMG). First described is a new-electric interface for virtual device control based on gesture recognition. The second development is a Bayesian method for decomposing EMG into individual motor unit action potentials. This more complex technique will then allow for higher resolution in separating muscle groups for gesture recognition. All examples presented rely upon sampling EMG data from a subject's forearm. The gesture based recognition uses pattern recognition software that has been trained to identify gestures from among a given set of gestures. The pattern recognition software consists of hidden Markov models which are used to recognize the gestures as they are being performed in real-time from moving averages of EMG. Two experiments were conducted to examine the feasibility of this interface technology. The first replicated a virtual joystick interface, and the second replicated a keyboard. Moving averages of EMG do not provide easy distinction between fine muscle groups. To better distinguish between different fine motor skill muscle groups we present a Bayesian algorithm to separate surface EMG into representative motor unit action potentials. The algorithm is based upon differential Variable Component Analysis (dVCA) [l], [2] which was originally developed for Electroencephalograms. The algorithm uses a simple forward model representing a mixture of motor unit action potentials as seen across multiple channels. The parameters of this model are iteratively optimized for each component. Results are presented on both synthetic and experimental EMG data. The synthetic case has additive white noise and is compared with known components. The experimental EMG data was obtained using a custom linear electrode array designed for this study.

Wheeler, Kevin R.↗

NASA NTRS2005

Fundamental Mistuning Model for Probabilistic Analysis Studied Experimentally

The Fundamental Mistuning Model (FMM) is a reduced-order model for efficiently calculating the forced response of a mistuned bladed disk. FMM ID is a companion program that determines the mistuning in a particular rotor. Together, these methods provide a way to acquire mistuning data in a population of bladed disks and then simulate the forced response of the fleet. This process was tested experimentally at the NASA Glenn Research Center, and the simulated results were compared with laboratory measurements of a "fleet" of test rotors. The method was shown to work quite well. It was found that the accuracy of the results depends on two factors: (1) the quality of the statistical model used to characterize mistuning and (2) how sensitive the system is to errors in the statistical modeling.

Griffin, Jerry H.↗

DOE OSTI2024

Tractometry of the Human Connectome Project: resources and insights

The Human Connectome Project (HCP) has become a keystone dataset in human neuroscience, with a plethora of important applications in advancing brain imaging methods and an understanding of the human brain. We focused on tractometry of HCP diffusion-weighted MRI (dMRI) data. We used an open-source software library (pyAFQ; https://yeatmanlab.github.io/pyAFQ) to perform probabilistic tractography and delineate the major white matter pathways in the HCP subjects that have a complete dMRI acquisition (n = 1,041). We used diffusion kurtosis imaging (DKI) to model white matter microstructure in each voxel of the white matter, and extracted tract profiles of DKI-derived tissue properties along the length of the tracts. We explored the empirical properties of the data: first, we assessed the heritability of DKI tissue properties using the known genetic linkage of the large number of twin pairs sampled in HCP. Second, we tested the ability of tractometry to serve as the basis for predictive models of individual characteristics (e.g., age, crystallized/fluid intelligence, reading ability, etc.), compared to local connectome features. To facilitate the exploration of the dataset we created a new web-based visualization tool and use this tool to visualize the data in the HCP tractometry dataset. Finally, we used the HCP dataset as a test-bed for a new technological innovation: the TRX file-format for representation of dMRI-based streamlines. We released the processing outputs and tract profiles as a publicly available data resource through the AWS Open Data program's Open Neurodata repository. We found heritability as high as 0.9 for DKI-based metrics in some brain pathways. We also found that tractometry extracts as much useful information about individual differences as the local connectome method. We released a new web-based visualization tool for tractometry—“Tractoscope” (https://nrdg.github.io/tractoscope). We found that the TRX files require considerably less disk space-a crucial attribute for large datasets like HCP. In addition, TRX incorporates a specification for grouping streamlines, further simplifying tractometry analysis.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Efficient screening of rare large pit anomalies on polished surfaces using a minimalist sampling scheme

Lawrence Livermore National Laboratory (LLNL) has made significant strides in generating clean energy through its inertial confinement fusion (ICF) experiments. These experiments rely on high-density carbon (HDC) coated shells to encapsulate the fusion fuel. The success of these experiments is heavily dependent on the surface quality of these shells, as even minor imperfections, such as deep pits, can negatively impact fusion yield. Ensuring the required smoothness involves an extensive surface-finishing process that spans approximately 20 stages, making it both time-intensive and resource-demanding. A critical challenge in this process is the need for high-resolution scans to detect rare deep pits, which can be costly and impractical if performed on every shell. This highlights the necessity of developing more efficient scanning methods to optimize time and cost without compromising accuracy. To address these challenges, we introduce a novel approach that employs the multivariate Dvoretzky–Kiefer–Wolfowitz (DKW) inequality to provide a probabilistic upper bound on the error in estimating pit distribution characteristics via a Kernel Density Estimator (KDE). This error bound enables efficient and reliable estimation of pit distribution characteristics at a specified statistical confidence level using a minimal number of surface scans. The integrated DKW-KDE approach was validated through surface-finishing experiments across two batches of HDC-coated shells, demonstrating consistent and robust performance across multiple stages of the surface-finishing experiments. The validation studies suggest that the integrated DKW-KDE approach achieves comparable accuracy in estimating the risk of deleterious large pits with six scans, thus conserving time and resources. Further evaluations show that performance remains consistent across batches and over multiple polishing stages. In conclusion, based on these findings, one can leverage the minimal-scan insights to strategically improve the bottleneck inspection process, thus enhancing the productivity and quality of shell polishing and similar challenging manufacturing processes.

Inertial confinement fusion↗

DOE OSTI2026

Uncertainty quantification and reliability assessment for intermodal freight transportation

Intermodal freight optimization models support cost-effective, low-emission, and timely goods movement by coordinating trucks, rail, and barges. These models determine optimal flows, routing, and modal switches while respecting infrastructure and operational constraints. However, their real-world utility is often undermined by pervasive uncertainties-such as fluctuating transportation costs and emissions, variable terminal capacities, and uncertain freight demand-that distort key performance outcomes, including total system cost, carbon footprint, and transit time reliability. This study presents a structured framework for quantifying uncertainty in intermodal freight transportation (IFT) optimization. The framework evaluates how input uncertainty affects system performance and reliability, a critical need for ensuring that model-based decisions remain robust under real-world variability, especially amid volatile fuel prices, shifting demand, and growing disruptions. It integrates three complementary methods: (1) Sobol-based global sensitivity analysis to identify influential parameters affecting cost, emissions, and transit time, (2) Monte Carlo-based capacity perturbation analysis to assess robustness under probabilistic facility disruptions, and (3) Monte Carlo filtering with Bayesian inference to detect threshold-based performance vulnerabilities. The results highlight diesel truck unit cost as the dominant driver of variability. To improve system resilience, planners should prioritize uncertainty in fuel-related parameters when designing intermodal strategies.

Intermodal freight transportation↗

DOE OSTI2022

General-Purpose Unsupervised Cyber Anomaly Detection via Non-Negative Tensor Factorization

Distinguishing malicious anomalous activities from unusual but benign activities is a fundamental challenge for cyber defenders. Prior studies have shown that statistical user behavior analysis yields accurate detections by learning behavior profiles from observed user activity. These unsupervised models are able to generalize to unseen types of attacks by detecting deviations from normal behavior, without knowledge of specific attack signatures. However, approaches proposed to date based on probabilistic matrix factorization are limited by the information conveyed in a two-dimensional space. Non-negative tensor factorization, on the other hand, is a powerful unsupervised machine learning method that naturally models multi-dimensional data, capturing complex and multi-faceted details of behavior profiles. Herein, our new unsupervised statistical anomaly detection methodology matches or surpasses state-of-the-art supervised learning baselines across several challenging and diverse cyber application areas, including detection of compromised user credentials, botnets, spam e-mails, and fraudulent credit card transactions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Estimating IDP Origins Using ACLED Political Violence Events: Validation with Lebanon IDP Flow Data

A key input in modeling population distribution and flows following conflict events is the inclusion of Internally Displaced Person (IDP) flows between administrative units within a country. These flows are critical for capturing population movement and redistribution driven by current events, particularly conflict. In some cases, IDP destination data are available while origin data is incomplete or unavailable. This creates a gap in understanding where displacement is occurring, limiting the ability to model population redistribution accurately. Without origin data, it is not possible to reallocate population flows or accurately represent where displacement is occurring within the country. This report evaluates whether Armed Conflict Location Event Data (ACLED) political violence event data can be used to estimate IDP origin distributions when direct origin data are unavailable. The approach is validated using historical IDP flow data from Lebanon, where both origins and destinations are observed. Results show that ACLED event distributions strongly correspond to observed IDP-origin patterns, particularly when using cumulative 60-day event windows. The method is most reliable for identifying major origin districts and approximating proportional origin shares. However, it is not intended to reconstruct exact individual displacement flows, but rather to provide a probabilistic spatial allocation of displacement origins.

99 GENERAL AND MISCELLANEOUS↗

NASA NTRS1984

Creep-rupture reliability analysis

A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTP's. A method is developed for evaluating material dependent constants for TTP's. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.

Peralta-Duran, A.↗

NASA NTRS1985

Creep-rupture reliability analysis

Peralta-Duran, A.↗

NASA NTRS2010

The Importance of HRA in Human Space Flight: Understanding the Risks

Human performance is critical to crew safety during space missions. Humans interact with hardware and software during ground processing, normal flight, and in response to events. Human interactions with hardware and software can cause Loss of Crew and/or Vehicle (LOCV) through improper actions, or may prevent LOCV through recovery and control actions. Humans have the ability to deal with complex situations and system interactions beyond the capability of machines. Human Reliability Analysis (HRA) is a method used to qualitatively and quantitatively assess the occurrence of human failures that affect availability and reliability of complex systems. Modeling human actions with their corresponding failure probabilities in a Probabilistic Risk Assessment (PRA) provides a more complete picture of system risks and risk contributions. A high-quality HRA can provide valuable information on potential areas for improvement, including training, procedures, human interfaces design, and the need for automation. Modeling human error has always been a challenge in part because performance data is not always readily available. For spaceflight, the challenge is amplified not only because of the small number of participants and limited amount of performance data available, but also due to the lack of definition of the unique factors influencing human performance in space. These factors, called performance shaping factors in HRA terminology, are used in HRA techniques to modify basic human error probabilities in order to capture the context of an analyzed task. Many of the human error modeling techniques were developed within the context of nuclear power plants and therefore the methodologies do not address spaceflight factors such as the effects of microgravity and longer duration missions. This presentation will describe the types of human error risks which have shown up as risk drivers in the Shuttle PRA which may be applicable to commercial space flight. As with other large PRAs of complex machines, human error in the Shuttle PRA proved to be an important contributor (~12 percent) to LOCV. An existing HRA technique was adapted for use in the Shuttle PRA, but additional guidance and improvements are needed to make the HRA task in space-related PRAs easier and more accurate. Therefore, this presentation will also outline plans for expanding current HRA methodology to more explicitly cover spaceflight performance shaping factors.

Hamlin, Teri↗