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Results for “Joint distribution”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Understanding Uncertainties in Tropical Cyclone Rainfall Hazard Modeling Using Synthetic Storms

Tropical cyclone (TC) rainfall hazard assessment is subject to the bias in TC climatology estimation from climate simulations or synthetic downscaling. In this study, we investigate the uncertainty in TC rainfall hazard assessment induced by this bias using both rain gauge and radar observations and synthetic-storm-model-coupled TC rainfall simulations. We identify the storm’s maximum intensity, impact duration, and minimal distance to the site to be the three most important storm parameters for TC rainfall hazard, and the relationship between the important storm parameters and TC rainfall can be well captured by a physics-based TC rainfall model. The uncertainty in the synthetic rainfall hazard induced by the bias in TC climatology can be largely explained by the bias in the important storm parameters simulated by the synthetic storm model. Correcting the distribution of the most biased parameter may significantly improve rainfall hazard estimation. Bias correction based on the joint distribution of the important parameters may render more accurate rainfall hazard estimations; however, the general technical difficulties in resampling from high-dimensional joint probability distributions prevent more accurate estimations in some cases. The results of the study also support future investigation of the impact of climate change on TC rainfall hazards through the lens of future changes in the identified important storm parameters.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1983

Radar modeling of space diversity associated with slant path rain attenuation at variable path angles, frequencies, and drop size distributions

Single and joint terminal slant path attenuation statistics at frequencies of 28.56 and 19.04 GHz were derived from radar data. Statistics were independently obtained for path angles of 20, 45, and 90 deg, in order to examine how path angle influences both single terminal and joint probability distributions. A prediction technique is demonstrated to work well for calculating both single and joint terminal distributions at other path angles. Diversity gains and autocorrelation function dependence on site spacing were determined employing the radar modeling results.

Goldhirsh, J.↗
DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗
NASA NTRS1997

Estimating the Uncertainty in Passive-Microwave Rain-Retrievals

Current passive-microwave rain-retrieval methods are largely based on databases built off-line using cloud models. The vertical distribution of hydrometeors within the cloud has a large impact on upwelling brightness temperatures ([31,[5]). Thus, a forward radiative transfer model can predict off-line the radiance associated with different rain scenarios. To estimate the rain from measured brightness temperatures, one simply looks for the rain scenario whose associated radiances are closest to the measurements. To understand the uncertainties in this process, we first study the dependence of the simulated brightness temperatures on different hydrometeor size distribution (DSD) models. We then analyze the marginal and joint distributions of the radiances observed by the Tropical Rainfall Measuring Mission satellite and of those in the databases used in the TRMM rain retrievals. We finally calculate the covariances of the rain profiles and brightness temperatures in the TRMM passive-microwave database and derive a simple parametric model for the conditional uncertainty, given measured radiances. These results are used to characterize the uncertainty inherent in the passive-microwave retrieval.

Coppens, Dorothee↗
DOE OSTI2021

Cosmological cross-correlations and nearest neighbour distributions

ABSTRACT Cross-correlations between data sets are used in many different contexts in cosmological analyses. Recently, k-nearest neighbour cumulative distribution functions (kNN-CDF) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of NN measurements to describe joint distributions of, and correlations between, two data sets. We describe the measurement of joint kNN-CDFs, and show that these measurements are sensitive to all possible connected N-point functions that can be defined in terms of the two data sets. We describe how the cross-correlations can be isolated by combining measurements of the joint kNN-CDFs and those measured from individual data sets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully non-linear cosmological data sets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through NN measurements are more sensitive to the underlying cosmological parameters, compared to traditional two-point cross-correlation measurements over the same range of scales. Finally, we demonstrate how the NN cross-correlations can robustly detect cross-correlations between sparse samples – the same regime where the two-point cross-correlation measurements are dominated by noise.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1988

Learning a Probability Distribution Efficiently and Reliably

A new algorithm, called the CDF-Inversion Algorithm, is described. Using it, one can efficiently learn a probability distribution over a finite set to a specified accuracy and confidence. The algorithm can be extended to learn joint distributions over a vector space. Some implementation results are described.

Laird, Philip↗
NASA NTRS1980

Statistical wind profile gust model

A statistical wind profile gust model for the Space Transportation Operations and Trade Studies is developed by using 1800 Jimsphere wind profile data collected at Cape Kennedy during 1965 to 1972. Wind profiles from the surface to 20 km in component form, i.e., zonal and meridional are processed through the digital filters of different wave length ranges bases on the Martin-Graham cosine rolloff model. The residuals obtained from the filtering processes for the data base for the statistical analysis. For each wind component the gust and gust length at a specified reference altitude in a residual profile are defined. A two parameter gamma probability marginal distribution seems to fit the component gust amplitude and the gust length when redefined. The problem of finding an appropriate bivariate joint distribution of the gust amplitude and length remains to be solved. The probability distribution of the modulus of the gust amplitudes was derived under the assumption that they are independently distributed as gamma variates.

Doss, D. C.↗
DOE OSTI2023

Modal Analysis of Ultrasonic Spot Welding for Lightweight Metals Joining

Ultrasonic spot welding (USW) represents one of the unique solid-state joining methods for lightweight materials such as magnesium alloy and aluminum alloy. However, the sonotrode vibration may have a detrimental impact on the sheet material and the existing welds, depending on the component geometry and vibration frequency. In this study, a modal analysis tool based on steady-state dynamics was developed for ultrasonic spot welding which features a cyclic load applied to the sheets during the joining process. Through predicting relative motion and shear stress at the faying surfaces, coupon geometry and weld spacing are identified as two major factors that affect the welding reliability and joint quality in USW. The model was validated via welding experiments on aluminum alloy and magnesium alloy and relevant characterization of temperature distribution, joint strength as well as fracture location.

36 MATERIALS SCIENCE↗
DOE OSTI2026

An Optimized Parameterization of Sub‐Grid Scale Advection for Convection Permitting Models

Convection‐permitting models (CPMs) explicitly resolve deep convection yet under‐resolve the organized lateral exchanges among drafts and their environment that control entrainment/detrainment, precipitation efficiency, and mesoscale structure. In this work, we introduce the Optimized Advection Scheme (OAS), which introduces a small rotation of the Cartesian frame of reference for the horizontal winds relative to other variables used in advection that induces cross‐gradient transport to mimic under‐resolved convective mixing. The rotation angle is selected to minimize the Kullback–Leibler divergence between the simulated and satellite observed precipitation intensity distributions, yielding a physically consistent perturbation that is computationally inexpensive and portable. Optimized Advection Scheme is implemented in WRF and evaluated over Amazon (April 2014). It shifts precipitation–precipitable‐water joint distributions toward lighter rain, reduces overly intense rates, and improves mesoscale convective system (MCS) lifetime and propagation. Mechanistically, the added cross‐gradient transport promotes convective detrainment and environmental mixing, which cools and moistens the mid‐troposphere, weakens downward momentum transport, alleviates excessive downwelling shortwave biases, and warms the surface temperature. The optimized rotation angle yields comparable improvements at 4‐km and 1‐km grid spacing, demonstrating resolution‐independent benefits across the CPM gray zone. By targeting the dynamical root of under‐mixed convective circulations, rather than tuning model microphysics or closures, OAS delivers robust, scale‐aware improvements in precipitation statistics, cloud vertical structure, and characteristics of MCS (MCSs), offering a practical pathway to more reliable CPM simulations for weather and climate applications.

CPM↗
DOE OSTI2023

The hidden structure of hydrodynamic transport in random fracture networks

We study the large-scale dynamics and prediction of hydrodynamic transport in random fracture networks. The flow and transport behaviour is characterized by first passage times and displacement statistics, which show heavy tails and anomalous dispersion with a strong dependence on the injection condition. The origin of these behaviours is investigated in terms of Lagrangian velocities sampled equidistantly along particle trajectories, unlike classical sampling strategies at a constant rate. The velocity series are analysed by their copula density, the joint distribution of the velocity unit scores, which reveals a simple, albeit hidden, correlation structure that can be described by a Gaussian copula. Based on this insight, we derive a Langevin equation for the evolution of equidistant particle speeds. In this framework, particle motion is quantified by a stochastic time-domain random walk, the joint density of particle position, and speed satisfies a Klein–Kramers equation. The upscaled theory quantifies particle motion in terms of the characteristic fracture length scale and the distribution of Eulerian flow velocities. That is, it is predictive in the sense that it does not require the a priori knowledge of transport attributes. The upscaled model captures non-Fickian transport features, and their dependence on the injection conditions in terms of the velocity point statistics and average fracture length. It shows that the first passage times and displacement moments are dominated by extremes occurring at the first step. The presented approach integrates the interaction of flow and structure into a predictive model for large-scale transport in random fracture networks.

42 ENGINEERING↗
NASA NTRS1982

Results of the VPI&SU Comstar experiment

This paper summarizes annual and cumulative attenuation data, depolarization data, and associated local rain rate distributions obtained with the Comstar family of 19.04- and 28.56-GHz satellite beacons during the years 1977-1981. It discusses the relationships between attenuation and rain rate and between attenuation and depolarization, compares measured data on the joint distribution of attenuation and depolarization, and examines the limitations that propagation effects will impose on future 20/30-GHz satellite communications systems.

Andrews, J. H.↗
DOE OSTI2020

The Evolving Distribution of Relative Humidity Conditional Upon Daily Maximum Temperature in a Warming Climate

Abstract The impacts of heat waves in a warming climate depend not only on changing temperatures but also on changing humidity. Using 35 simulations from the Community Earth System Model Large Ensemble (CESM LENS), we investigate the long‐term evolution of the joint distribution of summer relative humidity (RH) and daily maximum temperature ( Tmax ) near four U.S. cities (New York City, Chicago, Phoenix, and New Orleans) under the high‐emissions Representative Concentration Pathway (RCP) 8.5. We estimate the conditional quantiles of RH given Tmax with quantile regression models, using functions of temperature for each city in July for three time periods (1990–2005, 2026–2035, and 2071–2080). Quality‐of‐fit diagnostics indicate that these models accurately estimate conditional quantiles for each city. As expected, each quantile of Tmax increases from 1990–2005 to 2071–2080, while mean RH decreases modestly. Conditional upon a fixed quantile of Tmax , the median and high quantiles of RH decrease, while those of the Heat Index (HI) and dew point both increase. This result suggests that, despite a modest decrease in median relative humidity, heat stress measured by metrics considering both humidity and temperature in a warming climate will increase faster than that measured by temperatures alone would indicate. For a fixed Tmax , the high quantiles of RH (and thus of HI and dew point) increase from 1990–2005 to 2071–2080 in all four cities. This result suggests that the heat stress of a day at a given Tmax will increase in a warming climate due to the increase of RH.

Yuan, Jiacan↗
NASA NTRS1987

Probabilistic SSME blades structural response under random pulse loading

The purpose is to develop models of random impacts on a Space Shuttle Main Engine (SSME) turbopump blade and to predict the probabilistic structural response of the blade to these impacts. The random loading is caused by the impact of debris. The probabilistic structural response is characterized by distribution functions for stress and displacements as functions of the loading parameters which determine the random pulse model. These parameters include pulse arrival, amplitude, and location. The analysis can be extended to predict level crossing rates. This requires knowledge of the joint distribution of the response and its derivative. The model of random impacts chosen allows the pulse arrivals, pulse amplitudes, and pulse locations to be random. Specifically, the pulse arrivals are assumed to be governed by a Poisson process, which is characterized by a mean arrival rate. The pulse intensity is modelled as a normally distributed random variable with a zero mean chosen independently at each arrival. The standard deviation of the distribution is a measure of pulse intensity. Several different models were used for the pulse locations. For example, three points near the blade tip were chosen at which pulses were allowed to arrive with equal probability. Again, the locations were chosen independently at each arrival. The structural response was analyzed both by direct Monte Carlo simulation and by a semi-analytical method.

Shiao, Michael↗
DOE OSTI2021

Distributionally Robust Partially Observable Markov Decision Process with Moment-Based Ambiguity

In this paper, we consider a distributionally robust partially observable Markov decision process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations can be inferred using side information at the end of each period after an action being taken. We build an ambiguity set of the joint distribution using bounded moments via conic constraints and seek an optimal policy to maximize the worst-case (minimum) reward for any distribution in the set. We show that the value function of DR-POMDP is piecewise linear convex with respect to the belief state and propose a heuristic search value iteration method for obtaining lower and upper bounds of the value function. We conduct numerical studies and demonstrate the computational performance of our approach via testing instances of a dynamic epidemic control problem. Our results show that DR-POMDP can produce more robust policies under misspecified distributions of transition-observation probabilities as compared to POMDP but has less costly solutions than robust POMDP. The DR-POMDP policies are also insensitive to varying parameter in the ambiguity set and to noise added to the true transition-observation probability values obtained at the end of each decision period.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimizing High Performance Markov Clustering for Pre-Exascale Architectures

HipMCL is a high-performance distributed memory implementation of the popular Markov Cluster Algorithm (MCL) and can cluster large-scale networks within hours using a few thousand CPU-equipped nodes. It relies on sparse matrix computations and heavily makes use of the sparse matrix-sparse matrix multiplication kernel (SpGEMM). The existing parallel algorithms in HipMCL are not scalable to Exascale architectures, both due to their communication costs dominating the runtime at large concurrencies and also due to their inability to take advantage of accelerators that are increasingly popular. In this work, we systematically remove scalability and performance bottlenecks of HipMCL. We enable GPUs by performing the expensive expansion phase of the MCL algorithm on GPU. Additionally, we propose a CPU-GPU joint distributed SpGEMM algorithm called pipelined Sparse SUMMA and integrate a probabilistic memory requirement estimator that is fast and accurate. Furthermore, we develop a new merging algorithm for the incremental processing of partial results produced by the GPUs, which improves the overlap efficiency and the peak memory usage. We also integrate a recent and faster algorithm for performing SpGEMM on CPUs. We validate our new algorithms and optimizations with extensive evaluations. With the enabling of the GPUs and integration of new algorithms, HipMCL is up to 12.4x faster, being able to cluster a network with 70 million proteins and 68 billion connections just under 15 minutes using 1024 nodes of ORNL's Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

A Velocity Distribution Model for Steady State Heat Transfer

Consider a box that is filled with an ideal gas and that is aligned along Cartesian coordinates (x, y, z) having until length in the 'y' direction and unspecified length in the 'x' and 'z' directions. Heat is applied uniformly over the 'hot' end of the box (y = 1) and is removed uniformly over the 'cold' end (y = O) at a constant rate such that the ends of the box are maintained at temperatures T(sub 0) at y = O and T(sub 1) at y = 1. Let U, V, and W denote the respective velocity components of a molecule inside the box selected at some random time and at some location (x, y, z). If T(sub 0) = T(sub 1), then U, Y, and W are mutually independent and Gaussian, each with mean zero and variance RT(sub 0), where R is the gas constant. When T(sub 0) does not equal T(sub 1) the velocity components are not independent and are not Gaussian. Our objective is to characterize the joint distribution of the velocity components U, Y, and W as a function of y, and, in particular, to characterize the distribution of V given y. It is hoped that this research will lead to an increased physical understanding of the nature of turbulence.

Hall, Eric B.↗