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DOE OSTI2025

A New Probability Table Methodology with Covariances on Probability Tables

Through this work, we test a new methodology of evaluating probability tables informed by a combination of physics models and experimental data. This methodology uses generalized least squares to produce a joint mean and covariance for average cross sections and probability tables. This methodology has been tested and validated using total Monte Carlo. Attempts were made to parameterize the probability table using a formulation provided in. Although the normal inverse Gaussian fit was successful for the total cross section probability distribution, the rational-function fit to the capture, inelastic, and fission cross sections was unsuccessful due to time constraints.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Divide and conquer: separating the two probabilities in seismic phase picking

There are two fundamental probabilities in the seismic phase picking process—the probability of the existence of a seismic phase (detection probability) and the probability associated with the phase arrival time estimation (timing probability). The nearly ubiquitous approach in developing deep learning phase picking models is to use a kernel, such as a truncated Gaussian, to mask the labelled phase arrival time and train a segmentation model. Once a model is trained, the times of the peaks in the output are taken as phase arrival times (picks), and the height of the peaks are taken as ‘probability’ of the picks. Here, we show that this ‘probability’ represents neither the detection nor the timing probability because this approach forces the output to follow the shape of the kernel. We introduce an approach using two models to estimate these two distinct probabilities. We use a binary classifier with a calibrated confidence to address the detection probability and a multiclass classifier to obtain a probability mass function to address the timing probability. This new approach can make the deep learning-based phase picking process more interpretable and provide options to logically control seismic monitoring workflows.

58 GEOSCIENCES↗

DOE OSTI2026

Structural Aspects of Neutron Survival Probabilities

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Probability of Hydrogen Ignition: A Landscape Review and Gaps Assessment

The primary hazard of a leak from a hydrogen system is due to the immediate or delayed ignition of the fuel leading to a jet flame or explosion. Therefore, understanding the hydrogen ignition probability is critical for analyzing the risk of hydrogen systems. This report reviews the current understanding of hydrogen ignition mechanisms and methods for modeling their probability. The stoichiometry, ignition strength, and ignition source temperature are all important characteristics that can affect both the probability of ignition and the outcome of the subsequent combustion event. A brief review of diffusion ignition demonstrates that ignition probability models must account for seemingly spontaneous ignition of hydrogen in addition to scenarios where the ignition source is readily identified. State-of-the art models for both immediate and delayed ignition probabilities are presented, including different physical aspects of the scenarios (e.g., flow rate, ignition source characteristics) that are considered in the different modeling approaches. Current models often fail to account for the unique properties of hydrogen compared to other fuels, and most lack rigorous validation with hydrogen as a fuel. A fault tree framework is proposed to systematically evaluate the probability of ignition by integrating various ignition mechanisms and their uncertainties. Furthermore, this type of framework could enable additional insights into the most important mechanisms and would enable uncertainty quantification in risk assessment modeling. Recommendations for future research include the need for experimental validation of ignition models and the development of comprehensive methodologies that incorporate the specifics of hydrogen behavior in real-world scenarios.

hydrogen↗

DOE OSTI2026

Asymptotic inconsistency of the cumulative algorithm for laser-induced damage probability analysis

The “cumulative algorithm” is a data analysis method that has been proposed to provide an objective, nonparametric determination of laser-induced damage probability as a function of fluence from experimental data that contain both damaged sites and undamaged sites (i.e., 1-on-1 or S-on-1 testing protocols). In this work, the limitations of this approach are explored by considering the asymptotic limit of a large number of test sites. It is shown that the cumulative algorithm does not converge to the true probability distribution and significantly underestimates the damage probability near the damage onset. Here, based on the results of this work, the cumulative algorithm is not recommended for accurate estimation of damage probability.

Computational methods↗

DOE OSTI2025

Differential Seismic Phase Detection Probability as a Potential Discriminant of Explosions and Earthquakes

Deep learning models trained to estimate the probability of seismic P and S phases are rapidly expanding the scale of local event detections. Here, we evaluate the potential for deep learning model output phase detection probabilities to contribute to event‐type classification, particularly discrimination of single‐fired borehole explosions and earthquakes at local distances (<300 km). Motivated by the empirical success of P/S amplitude ratios, we consider the difference between P and S pick probability output from previously developed phase detection models, P prob −S prob ⁠, as a discriminant. Test data include M L ∼1–4 earthquakes and explosions observed by common seismographs in ten geologically diverse localities. Depending on the picking model and training data, binary classification using P prob −S prob with at least three stations can achieve approximately equivalent classification accuracy as P/S amplitude ratios without requiring any customization. Joint classification with P/S and P prob −S prob improves accuracy for most quality control scenarios. Pick probabilities are an efficient attribute to consider in explosion discrimination because they can be automated byproducts of event detection. They avoid the binary choice of picking or not picking weakly visible S waves common to explosions.

Duan, Chenglong [Rice Univ., Houston, TX (United S↗

NASA NTRS1957

Statistical Study of Aircraft Icing Probabilities at the 700- and 500- Millibar Levels over Ocean Areas in the Northern Hemisphere

A statistical study is made of icing data reported from weather reconnaissance aircraft flown by Air Weather Service (USAF). The weather missions studied were flown at fixed flight levels of 500 millibars (18,000 ft) and 700 millibars (10,000 ft) over wide areas of the Pacific, Atlantic, and Arctic Oceans. This report is presented as part of a program conducted by the NACA to obtain extensive icing statistics relevant to aircraft design and operation. The thousands of in-flight observations recorded over a 2- to 4-year period provide reliable statistics on icing encounters for the specific areas, altitudes, and seasons included in the data. The relative frequencies of icing occurrence are presented, together with the estimated icing probabilities and the relation of these probabilities to the frequencies of flight in clouds and cloud temperatures. The results show that aircraft operators can expect icing probabilities to vary widely throughout the year from near zero in the cold Arctic areas in winter up to 7 percent in areas where greater cloudiness and warmer temperatures prevail. The data also reveal a general tendency of colder cloud temperatures to reduce the probability of icing in equally cloudy conditions.

Perkins, Porter J.↗

DOE OSTI2025

First simultaneous measurement of the γ-ray and neutron emission probabilities in inverse kinematics at a heavy-ion storage ring

The probabilities for γ-ray and particle emission as a function of the excitation energy of a decaying nucleus are valuable observables for constraining the ingredients of the models that describe the deexcitation of nuclei near the particle emission threshold. These models are essential in nuclear astrophysics and applications. In this paper, we have for the first time simultaneously measured the γ-ray and neutron emission probabilities of 208 Pb. The measurement was performed in inverse kinematics at the Experimental Storage Ring (ESR) of the GSI/FAIR facility, where a 208 Pb beam interacted through the 208 Pb (p,p') reaction with a hydrogen gas jet target. Instead of detecting the γ rays and neutrons emitted by 208 Pb, we detected the heavy beamlike residues produced after γ and neutron emission. These heavy residues were fully separated by a dipole magnet of the ESR and were detected with outstanding efficiencies. The comparison of the measured probabilities with model calculations has allowed us to test and select different descriptions of the γ-ray strength function and the nuclear level density available in the literature.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Probability Density Function for the spatial and intensity distribution of neutron-induced defects in Silicon

The ability to model semiconductor device degradation under neutron irradiation depends upon having a robust modeling capability for the neutron-induced collision cascades as well as a means to analytically fit the resulting probability distributions of defect production and ionizing energy deposition for purposes of extrapolation to low-probability, high-consequence scenarios. In this paper, the widely-utilized binary collision approximation codes MARLOWE and SRIM are deployed in conjunction with a critical examination of their parameterizations as benchmarked against higher-fidelity molecular dynamics simulations. A simple 3-parameter form described by the Generalized Logistic Distribution is shown to be a good fit to Frenkel pair and ionization intensity distributions in bulk silicon. The BCA codes are then applied to simulate cascades in 5 nm layers of a representative gate-all-around nanosheet transistor, where joint probability distributions of threshold levels of damage to multiple layers are evaluated.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Assessing the Impact of Measurement Precision on Metabolite Identification Probability in Multidimensional Mass Spectrometry-Based, Reference-Free Metabolomics

Identification of compounds with minimal ambiguity remains a central challenge in mass spectrometry-based metabolomics. Conventional compound identification relies on comparing analytical signatures (e.g., mass-to-charge ratio, collision cross section, tandem mass spectra) against reference data obtained from measurements of authentic chemical standards. The breadth of annotatable compounds using this approach is necessarily limited by availability of authentic standards, analytical throughput, and resolving power of the separations that underly the measurements. The maturation of computational methods, both theory-driven and artificial intelligence/machine learning-based, for prediction of various molecular properties relevant to multidimensional mass spectrometry measurements has opened the door to a new “reference-free” paradigm of compound annotation. Through augmenting existing reference data for molecular properties with computational predictions, the universe of identifiable chemical species can be expanded significantly beyond its current limits. An unexplored aspect of this novel approach is understanding how to gauge confidence in resulting annotations, especially as the compound search space is expanded. Intuitively, the confidence of a compound annotation is related to the inherent discriminatory power of the molecular properties used for identification, as well as the precision with which the properties are measured or predicted. In this work, we characterize this relationship between measurement precision and identification probability in a systematic and quantitative fashion for a defined region of chemical space that includes organic small molecule metabolites. Importantly, this work establishes a framework for conducting metabolite identification probability analysis that enables others to quantify this relationship for their own compounds and properties of interest.

Metabolite Identification↗

DOE OSTI2026

Intrinsic nonlocality of spin- and polarization-resolved probabilities in strong-field quantum electrodynamics

Spin and polarization are central to precision tests of fundamental physics and for interpreting radiation from astrophysical sources and ultraintense laser-matter experiments. Here, focusing on the fundamental process of nonlinear Compton scattering, we demonstrate that a key assumption underlying current strong-field quantum electrodynamics models, i.e., that emission can be treated as an instantaneous random event sampled from a local differential rate, is inconsistent once emission angles, electron spin, and/or photon polarization are resolved. Namely, even in strictly constant and uniform fields , the resulting fully differential distribution is sign indefinite, yielding negative inferred probabilities. The physical reason is that the photon emission probability builds up over a finite length of the electron trajectory, the formation region, during which the electron direction changes by roughly the same small angle that defines the radiation cone. Therefore, we put forward a new method where we integrate over this formation region analytically to obtain a physically consistent electron spin and photon polarization model. We show that the implementation of our model is compatible with existing Monte Carlo and particle-in-cell workflows. Simulations of a GeV-class electron-laser collision accessible at current petawatt facilities and of emission in a pulsarlike magnetic field are shown to reveal spin and polarization patterns that differ even qualitatively from state-of-the-art local models. In particular, our new model predicts substantial angle-dependent circular photon polarization where the well-known collinear-emission approach yields none, and a pronounced helicity bias in the recoiling electrons absent from current predictions. These findings have direct implications for upcoming strong-field QED experiments and for interpreting polarized radiation from extreme astrophysical environments.

astrophysical electromagnetic fields↗

DOE OSTI2025

First Measurement of the Neutron-Emission Probability with a Surrogate Reaction in Inverse Kinematics at a Heavy-Ion Storage Ring

Neutron-induced reaction cross sections of short-lived nuclei are imperative to understand the origin of heavy elements in stellar nucleosynthesis and for societal applications, but their measurement is extremely complicated due to the radioactivity of the targets involved. One way of overcoming this issue is to combine surrogate reactions with the unique possibilities offered by heavy-ion storage rings. In this work, we describe the first surrogate-reaction experiment in inverse kinematics, which we successfully conducted at the Experimental Storage Ring (ESR) of the GSI/FAIR facility, using the 208 Pb⁢(p,p') reaction as a surrogate for neutron capture on 207 Pb. Thanks to the outstanding detection efficiencies possible at the ESR, we were able to measure for the first time the neutron-emission probability as a function of the excitation energy of 208 Pb. We have used this probability to select different descriptions of the γ -ray strength function and nuclear level density, and provide reliable results for the neutron-induced radiative capture cross section of 207 Pb at energies for which no experimental data exist.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Exceedance Probabilities and Recurrence Intervals for Extended Power Outages in the United States

This report provides estimates of recurrence intervals and conditional exceedance probabilities for major power outages by U.S. region between 2015 and 2021. Additionally, we provide estimates for grid management, particularly outages caused by California’s public safety power shutoffs (PSPS), and for natural outages caused by major hurricanes. Outage recurrence intervals are the average number of years between outage events, and conditional exceedance probabilities are the likelihoods that a customer who experiences a major power outage will experience an outage exceeding a given duration. Major outage events are those that affect 10,000 or more customers, as defined by the U.S. Department of Energy’s (DOE’s) Electric Emergency Incident and Disturbance Report, called OE-417 (DOE 2020). These results can be applied to determine the likelihood of experiencing long-duration outages, which can be integrated into cost-benefit analyses of resilience solutions and broader energy resilience studies.

Ericson, Sean [National Renewable Energy Laborator↗

DOE OSTI2026

Turbine Damage Probability

Damage probability maps for offshore wind turbines exposed to tropical cyclones (TCs) under both historical and future climate scenarios along the U.S. Atlantic and Gulf Coasts are presented in this dataset. TCs are generated using the Risk Analysis Framework for Tropical Cyclones (RAFT), forced by CMIP6 historical and future global climate simulations. Maximum wind speeds for 20- and 50-year TCs are processed through a fragility function specific to offshore wind (OSW) turbines in order to estimate the probability of damage – specifically yielding and buckling – based on wind speed intensity.

17 WIND ENERGY↗

DOE OSTI2026

Re-evaluating probable maximum precipitation estimates: sensitivity to transposition domains and storm rotation using modern datasets

This study examines the sensitivity of Probable Maximum Precipitation (PMP) estimates to key methodological decisions embedded in the legacy approach adopted in the U.S. National Weather Service Hydrometeorological Reports No. 51 and No. 52. Although widely used for infrastructure design and risk regulation, fundamental aspects of PMP estimation—such as storm sample size, transposition domain, maximization procedures, and storm rotation—remain poorly constrained and lack formal guidance. Using the Red Rock watershed in Iowa as a case study, and leveraging the 2002–2023 NOAA Analysis of Record for Calibration (AORC) precipitation dataset, we systematically evaluate how each methodological choice, individually and in combination, influences PMP estimates. Our findings demonstrate that PMP is not a fixed physical upper bound but rather a modeling construct shaped heavily by user-defined assumptions. Notably, PMP values derived from modern gridded rainfall datasets can be substantially higher than the legacy estimate used in the original spillway design for Red Rock Dam. Decisions regarding storm sample size, domain extent, climatological window, and particularly storm rotation all contributed to higher PMP estimates. Storm rotation alone—a loosely constrained element in the current PMP practice—can amplify PMP by more than 25%. These results reveal the lack of standardized bounds in current PMP workflows and the need for systematic sensitivity and uncertainty analysis. As PMP estimation shifts toward probabilistic approaches, incorporating physically meaningful storm attributes will be key to developing more transparent, defensible methods for dam safety and climate-resilient infrastructure.

Probable maximum precipitation↗

DOE OSTI2025

Probability Density Function Control of Frequency Fluctuations in Renewable-Rich Power Systems

The stochastic nature of renewable energy sources (RESs) necessitates treating power system frequency response as a random process with a nonstationary probability density function (PDF). Here, based upon the stochastic distribution control theory originated by the second author, this paper proposes a novel stochastic controller to improve the frequency PDF in power grids when integrating a large amount of RESs, thereby minimizing the effects of uncertainties and enhancing overall system stability. The key idea is to manipulate the controllable power generation resources so that the frequency PDF is make to follow a target PDF by using the stochastic distribution control theory originated by the second author. The proposed method can easily be plugged into existing automatic generation controls for multi-area transmission grids. The proposed method is validated via a modified Kundar's two area system and 240-bus Western Electricity Coordinating Council systems. The simulation results show that the proposed control shapes the frequency PDF narrower and sharper, leading to a notable improvement toward minimizing the effects of randomness and uncertainty during grid operation.

frequency↗

DOE OSTI2025

Converting sWeights to probabilities with density ratios

The use of machine learning approaches continues to have many benefits in experimental nuclear and particle physics. One common issue is generating training data which is sufficiently realistic to give reliable results. Here we advocate using real experimental data as the source of training data and demonstrate how one might subtract background contributions through the use of probabilistic weights which can be readily applied to training data. The sPlot formalism is a common tool used to isolate distributions from different sources. However, the negative sWeights produced by the sPlot technique can cause training problems and poor predictive power. This article demonstrates how density ratio estimation can be applied to convert sWeights to event probabilities, which we call drWeights. The drWeights can then be applied to produce the distributions of interest and are consistent with direct use of the sWeights. This article will also show how decision trees are particularly well suited to convert sWeights, with the benefit of fast prediction rates and adaptability to aspects of experimental data such as the data sample size and proportions of different event sources. We also show that a density ratio product approach in which the initial drWeights are reweighted by an additional converter gives substantially better results.

Glazier, Derek I. [Univ. of Glasgow, Scotland (Uni↗

DOE OSTI2025

Development and validation of a software for simulating γ-γ coincidence emission and detection probabilities

Gamma-gamma coincidence spectrometers have the potential to significantly enhance detection sensitivity for ultra-trace radionuclide measurements. The implementation of these spectrometers, however, is limited by the complexity of acquisition hardware, data processing and quantification. This work reports development of a novel radionuclide quantification software for γ-γ coincidence measurements. For any radionuclide, the software parses the Evaluated Nuclear Structure Data File (ENSDF) database, recursively simulating all possible γ-γ coincidence signatures and their respective emission and detection probabilities. Implemented using Python programming language, the software employs several strategies to boost overall computational performance. Since coincidence-based spectrometers are of notable interest in monitoring compliance for the Comprehensive Nuclear-Test-Ban Treaty (CTBT), the software’s execution was tested for 84 CTBT-relevant radionuclides. To date, the software has been experimentally validated for 15 radionuclides using the Advanced Radionuclide Gamma spectrOmeter (ARGO) at Pacific Northwest National Laboratory, USA (PNNL). Notably, the software can be operated in convergence mode, whereby coincidence detection efficiency’s convergence behavior can help avoid unreliable radionuclide activity estimates. With growing number of coincidence spectrometers worldwide, this paper aims to assist the radiation metrology community in developing similar software for their system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗