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Results for “Probability and statistics”

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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Probability of detection of defects in coatings with electronic shearography

The goal of this research was to utilize statistical methods to evaluate the probability of detection (POD) of defects in coatings using electronic shearography. The coating system utilized in the POD studies was to be the paint system currently utilized on the external casings of the NASA Space Transportation System (STS) Revised Solid Rocket Motor (RSRM) boosters. The population of samples was to be large enough to determine the minimum defect size for 90 percent probability of detection of 95 percent confidence POD on these coatings. Also, the best methods to excite coatings on aerospace components to induce deformations for measurement by electronic shearography were to be determined.

Maddux, Gary A.↗
NASA NTRS1995

Probability of detection of defects in coatings with electronic shearography

The goal of this research was to utilize statistical methods to evaluate the probability of detection (POD) of defects in coatings using electronic shearography. The coating system utilized in the POD studies was to be the paint system currently utilized on the external casings of the NASA space transportation system reusable solid rocket motor boosters. The population of samples was to be large enough to determine the minimum defect size for 90-percent POD of 95-percent confidence POD on these coatings. Also, the best methods to excite coatings on aerospace components to induce deformations for measurement by electronic shearography were to be determined.

Russell, S. S.↗
NASA NTRS1984

The oblique impact hypothesis and relative probabilities of lunar and Martian meteorites

The suggestion by Nyquist (1983) that shergottites and possibly other SNC (shergottites, nakhlites, and Chassigny) meteorites were launched from the Martian surface by the oblique impact of large meteoroids is further evaluated in the context of the subsequent discovery of a lunar meteorite. It is demonstrated that within calculational uncertainties and the current poorly known fall statistics of lunar and probable Martian meteorites, the oblique impact hypothesis provides a satisfactory explanation of the relative abundances of lunar, Martian, and other meteorites. It is noted that these results support the oblique-impact-on-Mars origin of SNC meteorites and satisfactorily explain the occurrence of a lunar meteorite.

Nyquist, L. E.↗
NASA NTRS1976

Comparison of rate one-half, equivalent constraint length 24, binary convolutional codes for use with sequential decoding on the deep-space channel

Virtually all previously-suggested rate 1/2 binary convolutional codes with KE = 24 are compared. Their distance properties are given; and their performance, both in computation and in error probability, with sequential decoding on the deep-space channel is determined by simulation. Recommendations are made both for the choice of a specific KE = 24 code as well as for codes to be included in future coding standards for the deep-space channel. A new result given in this report is a method for determining the statistical significance of error probability data when the error probability is so small that it is not feasible to perform enough decoding simulations to obtain more than a very small number of decoding errors.

Massey, J. L.↗
NASA NTRS1978

Hail risk model for solar collectors

This report presents the results of a study assessing the probability of solar arrays being struck by hailstones of various sizes as a function of geographic location and service life. The study complements parallel studies of solar array sensitivity to hail damage, the final objective being an estimate of the most cost effective level for solar array hail protection. A key element of this study involves the generation of a statistical model describing the probability of impact by hailstones of various sizes and estimating the mean time between hits.

Gonzalez, C.↗
NASA NTRS2010

Probabilistic Design Analysis (PDA) Approach to Determine the Probability of Cross-System Failures for a Space Launch Vehicle

Quantifying the probability of significant launch vehicle failure scenarios for a given design, while still in the design process, is critical to mission success and to the safety of the astronauts. Probabilistic risk assessment (PRA) is chosen from many system safety and reliability tools to verify the loss of mission (LOM) and loss of crew (LOC) requirements set by the NASA Program Office. To support the integrated vehicle PRA, probabilistic design analysis (PDA) models are developed by using vehicle design and operation data to better quantify failure probabilities and to better understand the characteristics of a failure and its outcome. This PDA approach uses a physics-based model to describe the system behavior and response for a given failure scenario. Each driving parameter in the model is treated as a random variable with a distribution function. Monte Carlo simulation is used to perform probabilistic calculations to statistically obtain the failure probability. Sensitivity analyses are performed to show how input parameters affect the predicted failure probability, providing insight for potential design improvements to mitigate the risk. The paper discusses the application of the PDA approach in determining the probability of failure for two scenarios from the NASA Ares I project

Shih, Ann T.↗
DOE OSTI2025

Rare events and Griffiths phases in topological quantum error correction

The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

classical statistical mechanics↗
NASA NTRS2014

Grid Resolution Study over Operability Space for a Mach 1.7 Low Boom External Compression Inlet

This paper presents a statistical methodology whereby the probability limits associated with CFD grid resolution of inlet flow analysis can be determined which provide quantitative information on the distribution of that error over the specified operability range. The objectives of this investigation is to quantify the effects of both random (accuracy) and systemic (biasing) errors associated with grid resolution in the analysis of the Lockheed Martin Company (LMCO) N+2 Low Boom external compression supersonic inlet. The study covers the entire operability space as defined previously by the High Speed Civil Transport (HSCT) High Speed Research (HSR) program goals. The probability limits in terms of a 95.0% confidence interval on the analysis data were evaluated for four ARP1420 inlet metrics, namely (1) total pressure recovery (PFAIP), (2) radial hub distortion (DPH/P), (3) ) radial tip distortion (DPT/P), and (4) ) circumferential distortion (DPC/P). In general, the resulting +/-0.95 delta Y interval was unacceptably large in comparison to the stated goals of the HSCT program. Therefore, the conclusion was reached that the "standard grid" size was insufficient for this type of analysis. However, in examining the statistical data, it was determined that the CFD analysis results at the outer fringes of the operability space were the determining factor in the measure of statistical uncertainty. Adequate grids are grids that are free of biasing (systemic) errors and exhibit low random (precision) errors in comparison to their operability goals. In order to be 100% certain that the operability goals have indeed been achieved for each of the inlet metrics, the Y+/-0.95 delta Y limit must fall inside the stated operability goals. For example, if the operability goal for DPC/P circumferential distortion is ≤0.06, then the forecast Y for DPC/P plus the 95% confidence interval on DPC/P, i.e. +/-0.95 delta Y, must all be less than or equal to 0.06.

Grid↗
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
DOE OSTI2025

TPCpp-10M: Simulated proton-proton collisions in a time projection chamber for AI foundation models

Scientific foundation models hold great promise for advancing nuclear and particle physics by improving analysis precision and accelerating discovery. Yet, progress in this field is often limited by the lack of openly available large scale datasets, as well as standardized evaluation tasks and metrics. Furthermore, the specialized knowledge and software typically required to process particle physics data pose significant barriers to interdisciplinary collaboration with the broader machine learning community. This work introduces a large, openly accessible dataset of 10 million simulated proton-proton collisions, designed to support self-supervised training of foundation models. To facilitate ease of use, the dataset is provided in a common NumPy format. In addition, it includes 70,000 labeled examples spanning three well defined downstream tasks: track finding, particle identification, and noise tagging, to enable systematic evaluation of the foundation model's adaptability. The simulated data are generated using the Pythia Monte Carlo event generator at a center of mass energy of $\sqrt{s}$ = 200 GeV and processed with Geant4 to include realistic detector conditions and signal emulation in the sPHENIX Time Projection Chamber at the Relativistic Heavy Ion Collider, located at Brookhaven National Laboratory. This dataset resource establishes a common ground for interdisciplinary research, enabling machine learning scientists and physicists alike to explore scaling behaviors, assess transferability, and accelerate progress toward foundation models in nuclear and high energy physics. The complete simulation and reconstruction chain is reproducible with the sPHENIX software stack. All data and code locations are provided under Data Accessibility.

Data Analysis, Statistics and Probability (physics↗
DOE OSTI2025

A comparison of probabilistic generative frameworks for molecular simulations

Generative artificial intelligence is now a widely used tool in molecular science. Despite the popularity of probabilistic generative models, numerical experiments benchmarking their performance on molecular data are lacking. Here, in this work, we introduce and explain several classes of generative models, broadly sorted into two categories: flow-based models and diffusion models. We select three representative models: neural spline flows, conditional flow matching, and denoising diffusion probabilistic models, and examine their accuracy, computational cost, and generation speed across datasets with tunable dimensionality, complexity, and modal asymmetry. Our findings are varied, with no one framework being the best for all purposes. In a nutshell, (i) neural spline flows do best at capturing mode asymmetry present in low-dimensional data, (ii) conditional flow matching outperforms other models for high-dimensional data with low complexity, and (iii) denoising diffusion probabilistic models appear the best for low-dimensional data with high complexity. Our datasets include a Gaussian mixture model and the dihedral torsion angle distribution of the Aib9 peptide, generated via a molecular dynamics simulation. We hope our taxonomy of probabilistic generative frameworks and numerical results may guide model selection for a wide range of molecular tasks.

Artificial intelligence↗
DOE OSTI2025

A hybrid neural architecture: Online attosecond x-ray characterization

The emergence of high-repetition-rate x-ray free-electron lasers (XFELs), such as SLAC’s LCLS-II, serves as our canonical example for autonomous controls that necessitate high-throughput diagnostics paired with streaming computational pipelines capable of single-shot analysis with extremely low latency. We present the deterministic characterization with an integrated parallelizable hybrid resolver architecture, a hybrid machine learning framework designed for fast, accurate analysis of XFEL diagnostics using angular streaking-based sinogram images. This architecture integrates convolutional neural networks and bidirectional long short-term memory models to denoise input, identify x-ray sub-spike features, and extract sub-spike relative delays with sub-30 attosecond temporal resolution. Deployed on low-latency hardware, it achieves over 10 kHz throughput with 168.3 μs inference latency, indicating scalability to 14 kHz with field-programmable gate array integration. By transforming regression tasks into classification problems and leveraging optimized error encoding, we achieve high precision with low-latency performance that is critical for real-time streaming event selection and experimental control feedback signals. This represents a key development in real-time control pipelines for next-generation autonomous science, generally, and high repetition-rate x-ray experiments in particular.

Accelerator Physics (physics.acc-ph)↗
DOE OSTI2026

Predictive models of the genetic bases underlying budding yeast fitness in multiple environments

Abstract The ability of organisms to adapt and survive depends on the effects of genes and the environment on fitness. However, the multigenic nature of fitness and genotype-by-environment interactions hinder our understanding of the genetic basis of fitness. Here, we established fitness prediction models for 35 environments using machine learning and existing fitness data and different genetic variant types for a Saccharomyces cerevisiae population. Models revealed that the predictive ability of genetic variants varied across environments, with copy number variants explaining the majority of fitness variation in most cases. Model interpretation showed that different variant types identified distinct gene sets associated with predictive variants. These gene sets were significantly enriched in experimentally validated genes affecting fitness in only a subset of environments, indicating that many genes influencing fitness remain unexplored. Notably, non-experimentally validated genes were more important than validated ones for fitness predictions. Gene contributions to predictions were both isolate- and environment-dependent, pointing to gene-by-gene and gene-by-environment interactions. Furthermore, models uncovered experimentally validated and novel candidate genetic interactions for a well-characterized stress, the fungicide benomyl. These findings highlight the feasibility of identifying the genetic basis of fitness by using different genetic variant types and offer novel targets for future functional analysis.

DNA copy number variations↗
DOE OSTI2025

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Data Analysis, Statistics and Probability (physics↗
NASA NTRS1971

Some sequential, distribution-free pattern classification procedures with applications

Some sequential, distribution-free pattern classification techniques are presented. The decision problem to which the proposed classification methods are applied is that of discriminating between two kinds of electroencephalogram responses recorded from a human subject: spontaneous EEG and EEG driven by a stroboscopic light stimulus at the alpha frequency. The classification procedures proposed make use of the theory of order statistics. Estimates of the probabilities of misclassification are given. The procedures were tested on Gaussian samples and the EEG responses.

Poage, J. L.↗