Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Probability Distribution Function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An update to the Sandia method for creating Typical Meteorological Years from a limited pool of calendar years

Typical Meteorological Years (TMYs) are essential for the efficient evaluation of energy system performance. Ideally, 30 years of weather data are required to generate TMYs, but significantly fewer years are typically available due to practical limitations. To address this issue, an update to the Sandia method was developed, referred to as the Argonne method, to create TMYs from a limited number of years. Furthermore, this method enhances candidate diversity by systematically shifting original candidate months forward or backward by specific days, creating an expanded pool of candidates. The effectiveness of the Argonne method was validated through statistical testing, comparison of monthly average weather parameters, and numerical simulations. The results demonstrate a high probability of identifying at least one shifted month whose cumulative distribution functions of weather parameters closely align with long-term distributions. In 67 % of all comparisons, the monthly average weather parameters in TMYs generated using the Argonne method exhibit better agreement with long-term averages than TMY3. Moreover, in 74 % of the 318 building simulation cases, the Argonne method outperforms TMY3 in estimating long-term average building heating and cooling demands. Therefore, the Argonne method effectively diversifies the candidate pool and produces typical years that provide more accurate estimations of long-term averages compared to TMY3 when only a limited pool of calendar years (10 years or fewer) is available.

Building energy modeling↗
DOE OSTI2026

Beam loss modeling and mitigation due to intra-beam stripping

Intra-Beam Stripping (IBS) is a critical beam loss mechanism in high-intensity H- linacs and presents a significant limitation to increasing beam power. This work presents a computational framework to evaluate and mitigate IBS-induced beam loss along the Spallation Neutron Source (SNS) LINAC. Our calculation is based on an analytic theory and involves evaluation of a 9D integral using the Monte-Carlo technique. We first benchmarked our calculations against simplified, analytically solvable cases. We then applied our algorithm to Gaussian bunches with a known probability density function (PDF). We next expanded our algorithm to arbitrary bunch distributions using the Neural Spline Flow (NSF) models trained on PyORBIT tracking data. In the future, we plan to validate our algorithm experimentally and apply it to design IBS mitigation strategies.

Nln, Shivam [ORNL]↗
DOE OSTI2024

Computing the Instantaneous Collision Probability between Satellites using Characteristic Function Inversion

The probability that two satellites overlap in space at a specified instant of time is called their instantaneous collision probability. Assuming Gaussian uncertainties and spherical satellites, this probability is the integral of a Gaussian distribution over a sphere. This paper shows how to compute the probability using an established numerical procedure called characteristic function inversion. The collision probability in the short-term encounter scenario is also evaluated with this approach, where the instant at which the probability is computed is the time of closest approach between the objects. Python and R code is provided to evaluate the probability in practice. Overall, the approach has been established for over fifty years, is implemented in existing software, does not rely on analytical approximations, and can be used to evaluate two and three dimensional collision probabilities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Bayesian reconstruction of anisotropic flow fluctuations at fixed impact parameter

The cumulants of the distribution of anisotropic flow are measured accurately in Pb+Pb collisions at the LHC as a function of centrality classifiers (charged multiplicity and/or transverse energy). Using Bayesian inference, we reconstruct from these measurements the probability distribution of anisotropic flow in the ``theorists' frame'' where the impact parameter has a fixed magnitude and orientation, up to ∼70% centrality. The variation of flow fluctuations with impact parameter displays direct evidence of viscous damping, which is larger for higher Fourier harmonics, in line with expectations from hydrodynamics. We use intensive measures of non-Gaussian flow fluctuations, which have reduced dependence on centrality. Here, we infer from ATLAS data the magnitude of these intensive non-Gaussianities in each Fourier harmonic. They provide data-driven estimates of response coefficients to initial anisotropies, without resorting to any specific microscopic model of initial conditions. These estimates agree with viscous hydrodynamic calculations.

Bayesian methods↗
DOE OSTI2024

A Corrected Score Function Framework for Modelling Circadian Gene Expression

Many biological processes display oscillatory behaviour based on an approximately 24 h internal timing system specific to each individual. One process of particular interest is gene expression, for which several circadian transcriptomic studies have identified associations between gene expression during a 24 h period and an individual's health. A challenge with analysing data from these studies is that each individual's internal timing system is offset relative to the 24 h day-night cycle, where day–night cycle time is recorded for each collected sample. Laboratory procedures can accurately determine each individual's offset and determine the internal time of sample collection. However, these laboratory procedures are labour-intensive and expensive. Here, in this paper, we propose a corrected score function framework to obtain a regression model of gene expression given internal time when the offset of each individual is too burdensome to determine. A feature of this framework is that it does not require the probability distribution generating offsets to be symmetric with a mean of zero. Simulation studies validate the use of this corrected score function framework for cosinor regression, which is prevalent in circadian transcriptomic studies. Illustrations with data from three circadian transcriptomic studies further demonstrate that the proposed framework consistently mitigates bias relative to using a score function that does not account for this offset.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Supersaturation, Nucleation, and Phase Separation of Mesoscopic Systems

Supersaturation, nucleation, and phase separation are ubiquitous phenomena of great interest in both science and industry. However, a unified, quantitative understanding of these phenomena has yet to be achieved for mesoscopic systems. Here, we present a set of general equations that determine the monomer saturation degree, the size distribution, and the free energy of mesoscopic systems, as well as their phase-transition conditions. These equations reveal that, under supersaturation, the largest cluster size (LCS) is an important state variable; the supersaturation degree decreases with the LCS, approaching unity in the macroscopic limit. We identify the critical supersaturation, at which the nuclei undergo the phase transition to form large crystals. Below this critical supersaturation, the nucleus size distribution is either a unimodal function or a monotonically decreasing function of size, depending on the system and temperature. We also predict the most probable nucleus size and the direction of spontaneous changes of the LCS. Our theory provides a unified, quantitative explanation of the nucleus-size-distribution across six different systems, including nanoparticles and biological condensates. This work serves as a general theoretical framework useful for understanding and designing nucleation and phase transitions of mesoscopic systems.

Kang, Jingyu↗
DOE OSTI2024

Multilabel proportion prediction and out-of-distribution detection on gamma spectra of short-lived fission products

In the machine learning problem of multilabel classification, the objective is to determine for each test instance which classes the instance belongs to. In this work, we consider an extension of multilabel classification, called multilabel proportion prediction, in the context of radioisotope identification (RIID) using gamma spectra data. We aim to not only predict radioisotope proportions, but also identify out-of-distribution (OOD) spectra. We achieve this goal by viewing gamma spectra as discrete probability distributions, and based on this perspective, we develop a custom semi-supervised loss function that combines a traditional supervised loss with an unsupervised reconstruction error function. Our approach was motivated by its application to the analysis of short-lived fission products from spent nuclear fuel. In particular, we demonstrate that a neural network model trained with our loss function can successfully predict the relative proportions of 37 radioisotopes simultaneously. The model trained with synthetic data was then applied to measurements taken by Pacific Northwest National Laboratory (PNNL) to conduct analysis typically done by subject-matter experts. Here, we also extend our approach to successfully identify when measurements are OOD, and thus should not be trusted, whether due to the presence of a novel source or novel proportions.

Anomaly detection↗
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

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Likelihood-Based Particle Identification in the Short-Baseline Near Detector

Accurate particle identification is crucial in any high-energy physics experiment, allowing scientists to understand the unique interactions and mechanisms at play in a detector. In this project, I develop and study a new particle identification (PID) algorithm for the Short-Baseline Near Detector, a likelihood-based approach, different from out current $\chi^2$ method. A likelihood estimation offers a more physically motivated strategy for PID. The distribution random energy losses of charged particles traveling through a medium are described by the Vavilov probability density function. By using this model, we can account for random energy losses and construct likelihood functions specific to each particle type, potentially enabling a more accurate method for PID.

Vanderwaal, Sophia [U. Alabama, Huntsville] (ORCID↗
DOE OSTI2024

Direct numerical simulations of three-component Rayleigh–Taylor mixing and an improved model for multicomponent reacting mixtures

We present direct numerical simulations of a three-layer Rayleigh–Taylor instability (RTI) problem with a configuration based on the experiments of Suchandra & Ranjan ( J. Fluid Mech. , vol. 974, 2023, A35) and Jacobs & Dalziel ( J. Fluid Mech. , vol. 542, 2005, pp. 251–279). The problem consists of a layer of light fluid between two layers of heavy fluid with an Atwood number of 0.3. These simulations are first validated through comparison with available experimental data. The validated simulations are then utilized to analyse statistics in this three-component flow. First, length scales are examined utilizing spectra and two-point spatial correlations of velocity and species concentration fluctuations. Next, joint probability density functions (p.d.f.s) of species concentration are compared against several model p.d.f.s representing generalizations of the bivariate beta distribution. Notably, the joint p.d.f.s do not appear to be accurately described by a Dirichlet distribution, indicating the marginal distributions do not conform to a beta distribution. Finally, similarity of the present configuration to three-component mixing found in inertial confinement fusion (ICF) applications is exploited to develop and validate an improved model for the impact of multicomponent mixing on thermonuclear (TN) reaction rates. A single time instant from the present simulations is chosen for a TN burn calculation under the hypothetical assumption of ICF materials and temperatures. Total TN output from this second calculation is then compared against the prediction of the improved model. The new model is found to accurately predict TN reaction rates in both premixed and non-premixed configurations.

42 ENGINEERING↗
DOE OSTI2024

Quantum Random Walk Simulator Using Ultrafast Optical Switches

Quantum random walk processes have many intriguing applications in high energy physics including the simulation of parton shower evolution. We will present the design and initial results of a fiber loop time-bin quantum walk architecture using the hardware platform already in operation at the Fermilab Quantum Network in which the state of the photon is defined by its time-of-arrival. The fiber loop consists of an unbalanced Mach-Zehnder interferometer implemented using an ultrafast electro-optical switch. The input switch controls the photon path within the interferometer, while the output switch will direct the photon back into the interferometer or to single photon detectors to measure the probability distribution of arrival times. Depending on which path the photon takes each pass through the loop, its wave function will interfere on these optical switches similar to quantum interference on a beam splitter. This work is an important step towards utilizing real-world advantages of quantum information protocols to solve problems in high energy physics.

Cameron, Andrew [Fermilab]↗
DOE OSTI2025

Fast HARDI Uncertainty Quantification and Visualization with Spherical Sampling

In this paper, we study uncertainty quantification and visualization of orientation distribution functions (ODF), which corresponds to the diffusion profile of high angular resolution diffusion imaging (HARDI) data. The shape inclusion probability (SIP) function is the state‐of‐the‐art method for capturing the uncertainty of ODF ensembles. The current method of computing the SIP function with a volumetric basis exhibits high computational and memory costs, which can be a bottleneck to integrating uncertainty into HARDI visualization techniques and tools. We propose a novel spherical sampling framework for faster computation of the SIP function with lower memory usage and increased accuracy. In particular, we propose direct extraction of SIP isosurfaces, which represent confidence intervals indicating spatial uncertainty of HARDI glyphs, by performing spherical sampling of ODFs. Our spherical sampling approach requires much less sampling than the state‐of‐the‐art volume sampling method, thus providing significantly enhanced performance, scalability, and the ability to perform implicit ray tracing. Our experiments demonstrate that the SIP isosurfaces extracted with our spherical sampling approach can achieve up to 8164× speedup, 37282× memory reduction, and 50.2% less SIP isosurface error compared to the classical volume sampling approach. We demonstrate the efficacy of our methods through experiments on synthetic and human‐brain HARDI datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Generalized approach for rapid entropy calculation of liquids and solids

We build a comprehensive methodology for the fast computation of entropy across both solid and liquid phases. The proposed method utilizes a single trajectory of molecular dynamics (MD) to facilitate the calculation of entropy, which is composed of three components. The electronic entropy is determined through the temporal average acquired from density functional theory MD simulations. The vibrational entropy, typically the predominant contributor to the total entropy, even within the liquid state, is evaluated by computing the phonon density of states via the velocity autocorrelation function. The most arduous component to quantify, the configurational entropy, is assessed by probability analysis of the local structural arrangement and atomic distribution. We illustrate, through a variety of examples, that this method is both a versatile and valid technique for characterizing the thermodynamic states of both solids and liquids. Furthermore, this method is employed to expedite the calculation of melting temperatures, demonstrating its practical utility in computational thermodynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2026

A Framework for Parametric and Predictive Uncertainty Quantification in the E3SM Land Model: Assessing Site and Observable Generalizability

Quantifying parametric uncertainty using observations from individual sites provides a critical foundation for Earth system modeling, serving as a necessary first step before scaling up to regional or global applications. This study introduces a novel computational framework designed to enhance model predictability by reducing parametric uncertainty and assessing site and observable generalizability using various observational constraints. The framework integrates five components: Model Simulation, Statistical Emulation, Global Sensitivity Analysis (GSA), Model Calibration, and Model Prediction. Using the E3SM land model, we simulated site-level land-atmosphere carbon and energy fluxes from 2003 to 2007 across five evergreen needleleaf FLUXNET sites, perturbing 26 vegetation-related model parameters. Gaussian process emulators were employed to expedite GSA and model calibration. Four critical parameters that strongly influence selected land-atmosphere fluxes were identified by GSA. Bayesian approaches were used to infer parameter probability distributions leveraging synthetic data and FLUXNET observations. The results reveal that posterior parameter distributions vary significantly across different sites and observables within the same plant functional type. Probabilistic predictions indicate that parameters calibrated at one site can enhance predictive accuracy at other sites, although site heterogeneity may sometimes outweigh parametric uncertainty. Additionally, the probabilistic predictions demonstrate that calibration for one variable can also improve predictability for other variables, thereby maximizing predictive capabilities with limited observations. This framework provides a powerful approach for reducing parametric uncertainty in Earth system models and deepening our understanding of carbon dynamics and energy cycles. Its adaptability makes it a valuable tool for broader applications in Earth system modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Coverage, repulsion, and reactivity of hydrogen on High-Entropy alloys

Modeling hydrogen evolution reaction (HER) activity probability on IrPdPtRhRu(1 1 1) high-entropy alloys. Determining hydrogen coverages based on ligand effects and generalized hydrogen–hydrogen repulsion. The rate of H 2 formation is highly impacted by the level of hydrogen coverage on the catalyst surface. In search of optimal catalytic properties high-entropy alloys (HEA) are promising candidates that utilize the compositional space of multiple elements. Based on simulations of HEA model (1 1 1) surfaces with a range of hydrogen coverages, distributions of binding energies are used to construct a framework that approximates the probability that adsorbed hydrogen may lead to the formation of H 2 as a function of applied potential. By optimizing the alloy compositions for the highest activity probability at given potentials the best and most efficient catalyst candidates for HER can be identified. Treating hydrogen–hydrogen repulsion effects and binding energy separately, we find that the repulsion is larger for HEAs than for pure metals. Differing isotherm slopes in the mean adsorption and desorption energies demonstrate a possible hysteresis for hydrogen adsorption on HEAs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

New Measurements of the Deuteron-to-Proton 𝐹 2 Structure-Function Ratio

Nucleon structure functions, as measured in lepton-nucleon scattering, have historically provided a critical observable in the study of partonic dynamics within the nucleon. However, at very large parton momenta, it is both experimentally and theoretically challenging to extract parton distributions due to the probable onset of nonperturbative contributions and the unavailability of high-precision data at critical kinematics. Extraction of the neutron structure and the d quark distribution have been further challenging because of the necessity of applying nuclear corrections when utilizing scattering data from a deuteron target to extract the free neutron structure. However, a program of experiments has been carried out recently at the energy-upgraded Jefferson Lab electron accelerator aimed at significantly reducing the nuclear correction uncertainties on the d quark distribution function at large partonic momentum. This allows leveraging the vast body of deuterium data covering a large kinematic range to be utilized for d quark parton distribution function extraction. In this Letter, we present new data from experiment E12-10-002, carried out in Jefferson Lab Experimental Hall C, on the deuteron to proton cross section ratio at large Bjorken 𝑥. These results significantly improve the precision of existing data and provide a first look at the expected impact on quark distributions extracted from parton distribution function fits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗