Search NASA⌕ Search

SEARCH · Search NASA

Results for “integral probability metrics”

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 19 records

Stability and Convergence of Solutions to Stochastic Inverse Problems Using Approximate Probability Densities

Data-consistent inversion is designed to solve a class of stochastic inverse problems where the solution is a pullback of a probability measure specified on the outputs of a quantities of interest (QoI) map. Here, this work presents stability and convergence results for the case where finite QoI data result in an approximation of the solution as a density. Given their popularity in the literature, separate results are proven for three different approaches to measuring discrepancies between probability measures: f-divergences, integral probability metrics, and L p metrics. In the context of integral probability metrics, we also introduce a pullback probability metric that is well-suited for data-consistent inversion. This fills a theoretical gap in the convergence and stability results for data-consistent inversion that have mostly focused on convergence of solutions associated with approximate maps. Numerical results are included to illustrate key theoretical results with intuitive and reproducible test problems that include a demonstration of convergence in the measure-theoretic "almost" sense.

97 MATHEMATICS AND COMPUTING↗

Continuum shock mixture models for Ni+Al multilayers: Inert mesoscale simulations

Mesoscale modeling of shock waves in Ni+Al multilayers poses significant challenges that are due, in part, to shock-induced chemical reactions. Current modeling approaches utilize reactive molecular dynamics (MD), but they are limited to resolving domains of only a few hundred nanometers. In contrast, actual multilayer superlattices can be tens of micrometers thick, and they exhibit non-ideal (i.e., wavy) interfaces. The second part of our research builds upon previous work developing physically based, thermodynamically complete equations of state for various Ni and Al intermetallic compositions. Here, we introduce a novel workflow for high-fidelity mesoscale simulations of Ni+Al multilayers using a continuum hydrocode. By increasing the simulation domain size beyond MD limitations (e.g., 2 × 6 μm 2 ) and incorporating explicit interfacial roughness, we investigate the shock response of Ni+Al multilayers at previously unexplored scales. Our experimental design encompasses nine multilayer geometries with varying roughness amplitudes and tilt angles (θ = 15°, 30°, and 45°), alongside 19 flyer impact velocities ranging from 0.3 to 3.0 km/s, resulting in a total of 171 high-fidelity simulations. The bulk shock state from inert 2D mesoscale simulations aligns with the law of mixtures, while temperature and pressure fluctuations strongly correlate with multilayer geometry types. A new metric dubbed the “hot spot probability integral” shows a greater dependence on a tilt angle than interfacial roughness.

Kittell, David E. [Sandia National Laboratories (S↗

A Resilient Integrated Resource Planning Framework for Transmission Systems: Analysis and Optimization

This article presents a resilient Integrated Resource Planning (IRP) framework designed for transmission systems, with a specific focus on analyzing and optimizing responses to High-Impact Low-Probability (HILP) events. The framework aims to improve the resilience of transmission networks in the face of extreme events by prioritizing the assessment of events with significant consequences. Unlike traditional reliability-based planning methods that average the impact of various outage durations, this work adopts a metric based on the proximity of outage lines to generators to select HILP events. The system’s baseline resilience is evaluated by calculating load curtailment in different parts of the network resulting from HILP outage events. The transmission network is represented as an undirected graph. Graph-theoretic techniques are used to identify islands with or without generators, potentially forming segmented grids or microgrids. This article introduces Expected Load Curtailment (ELC) as a metric to quantify the system’s resilience. The framework allows for the re-evaluation of system resilience by integrating additional generating resources to achieve desired resilience levels. Optimization is performed in the re-evaluation stage to determine the optimal placement of distributed energy resources (DERs) for enhancing resilience, i.e., minimizing ELC. Case studies on the IEEE 24-bus system illustrate the effectiveness of the proposed framework. In the broader context, this resilient IRP framework aligns with energy sustainability goals by promoting robust and resilient transmission networks, as the optimal placement of DERs for resilience enhancement not only strengthens the system’s ability to withstand and recover from disruptions but also contributes to efficient resource utilization, advancing the overarching goal of energy sustainability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A spatial evaluation of Arctic sea ice and regional limitations in CMIP6 historical simulations

The Arctic sea ice response to a warming climate is assessed in a subset of models participating in Phase 6 of the Coupled Model Intercomparison Project (CMIP6), using several metrics in comparison with satellite observations and results from the Pan-Arctic Ice Ocean Modeling and Assimilation System and the Regional Arctic System Model. Our study examines the historical representation of sea ice extent, volume, and thickness using spatial analysis metrics, such as the integrated ice-edge error, Brier score, and Spatial Probability Score. We find that the CMIP6 multi-model mean captures the mean annual cycle and 1979-2014 sea ice trends remarkably well. However, individual models experience a wide range of uncertainty in the spatial distribution of sea ice when compared against satellite measurements and reanalysis data. Our metrics expose common and individual regional model biases, which sea ice temporal analyses alone do not capture. We identify large ice edge and ice thickness errors in Arctic sub-regions, implying possible model specific limitations in or lack of representation of some key physical processes. We postulate that many of them could be related to the oceanic forcing, especially in the marginal and shelf seas, where seasonal sea ice changes are not adequately simulated. We therefore conclude that an individual model’s ability to represent the observed/reanalysis spatial distribution still remains a challenge. We propose the spatial analysis metrics as useful tools to diagnose model limitations, narrow down possible processes affecting them, and guide future model improvements critical to the representation and projections of Arctic climate change.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Risk-Driven Probabilistic Approach to Quantify Resilience in Power Distribution Systems

It is of growing concern to ensure resilience in power distribution systems to extreme weather events. However, there are no clear methodologies or metrics available for resilience assessment that allows system planners to assess the impact of appropriate planning measures and new operational procedures for resilience enhancement. In this paper, we propose a resilience metric using parameters that define system attributes and performance. To represent extreme events (tail probability), the conditional value-at-risk of each of the parameters are combined using Choquet Integral to evaluate the overall resilience. The effectiveness of the proposed resilience metric is studied within the simulation-based framework under extreme weather scenarios with the help of a modified IEEE 123-bus system. With the proposed framework, system operators will have additional flexibility to prioritize one investment over the others to enhance the resilience of the grid.

Poudyal, Abodh↗

Microgrid Resilience: A Holistic and Context-Aware Resilience Metric

Microgrids present an effective solution for the coordinated deployment of various distributed energy resources and furthermore provide myriad additional benefits such as resilience, decreased carbon footprint, and reliability to energy consumers and the energy system as a whole. Boosting the resilience of distribution systems is another major benefit of microgrids. This is because they can also serve as a backup power source when the utility grid's operations are interrupted due to either high-probability low-impact events like a component failure or low-probability high-impact events - be it a natural disaster or a planned cyberattack. However, the degree to which any particular system can defend, adapt, and restore normal operation depends on various factors including the type and severity of events to which a microgrid is subjected. These factors, in turn, are dependent on the geographical location of the deployed microgrid as well as the cyber risk profile of the site where the microgrid is operating. Therefore, in this work, we attempt to capture this multi-dimensional interplay of various factors in quantifying the ability of the microgrid to be resilient in these varying aspects. This paper, thus, proposes a customized site-specific quantification of the resilience strength for the individual microgrid's capability to absorb, restore, and adapt to the changing circumstances for sustaining the critical load when a low-probability high-impact event occurs - termed as - context-aware resilience metric. We also present a case study to illustrate the key elements of our integrated analytical approach.

microgrid↗

Detecting defects that reduce breakdown voltage using machine learning and optical profilometry

Abstract Semiconductor wafer manufacturing relies on the precise control of various performance metrics to ensure the quality and reliability of integrated circuits. In particular, GaN has properties that are advantageous for high voltage and high frequency power devices; however, defects in the substrate growth and manufacturing are preventing vertical devices from performing optimally. This paper explores the application of machine learning techniques utilizing data obtained from optical profilometry as input variables to predict the probability of a wafer meeting performance metrics, specifically the breakdown voltage (V bk ). By incorporating machine learning techniques, it is possible to reliably predict performance metrics that cause devices to fail at low voltage. For diodes that fail at a higher (but still below theoretical) breakdown voltage, alternative inspection methods or a combination of several experimental techniques may be necessary.

42 ENGINEERING↗

Probabilistic Evaluation of Geomechanical Risks in CO2 Storage: An Exploration of Caprock Integrity Metrics Using a Multilaminate Model

The probabilistic uncertainty assessment of geomechanical risk—specifically, caprock failure—attributable to CO2 injection, as presented in a simplified hypothetical geological model, was the focus of this study. Our approach amalgamates the implementation of a multilaminate model, the creation of a response surface model in conjunction with the Box–Behnken sampling design, the execution of associated numerical modeling experiments, and the utilization of Monte Carlo simulations. Probability distributions to encapsulate the inherent variability (elastic and mechanical properties of the caprock and reservoir) and uncertainty in prediction estimates (vertical displacement, total strain, and F value) were employed. Our findings reveal that the Young modulus of the caprock is a key factor controlling equivalent total strain but is insufficient as a stand-alone indicator of caprock integrity. It is confirmed that the caprock can accommodate significant deformation without failure, if it possesses a low Young’s modulus and high mechanical strength properties, such as the friction angle and uniaxial compressive strength. Similarly, vertical displacement was found to be an unreliable indicator for caprock integrity, as caprock failure can occur across a broad spectrum of vertical displacements, particularly when both the Young modulus and mechanical strength properties have wide ranges. This study introduces the F value as the most dependable indicator for caprock failure, although it is a theoretical attribute (the shortest distance between the Mohr circle and the nearest failure envelope used to measure the sensitivity to failure) and not physically measurable in the field. Deviatoric stress levels were found to vary based on stress regimes, with the maximum levels observed under extensive and compressive stress regimes. In conjunction with the use of the response surface method, this study demonstrates the efficacy of the multilaminate framework and the Mohr–Coulomb constitutive model in providing a simplified, yet effective, probabilistic model of the mechanical behavior of caprock failure, reducing mathematical and computational complexities.

Energy & Fuels↗

JGI-Trichoderma v1.0

There is a series of Python and bash scripts to parse genomics datasets used to evaluate the coevolution of gene families and the feature importance of gene families using an SVM classifier. - Cover analysis: takes a list of single-copy genes in a set of genomes, aligns and builds the gene trees to determine if two gene families have a signature of covariation with one another. It parses the files to run phykit cover script described here: https://jlsteenwyk.com/PhyKIT/usage/index.html - SVM-classifier: This Python script is an SVM-based genomic classifier designed for biological data analysis. It combines machine learning with feature selection to identify important genomic markers and classify biological samples. Core Functionality: The script uses Support Vector Machines from scikit-learn to classify genomic data, incorporating SelectKBest for automated feature selection and leave-one-out cross-validation for performance assessment. It operates in multiple modes: feature ranking, optimal combination discovery, and sample prediction. Primary Applications: Genomic sample classification and biomarker discovery Feature importance analysis in high-dimensional biological datasets Prediction of sample categories based on genomic profiles Research applications requiring robust classification of biological data Key Advantages: High-dimensional handling: SVMs excel with genomic data's typical high feature-to-sample ratios Integrated feature selection: Reduces noise and computational overhead while identifying key markers Probability estimation: Provides confidence scores essential for biological interpretation Validation robustness: Leave-one-out cross-validation ensures reliable performance metrics Operational flexibility: Multiple analysis modes support different research phases from exploration to prediction

Stecca Steindorff, Andrei [Lawrence Berkeley Natio↗

Trade can buffer climate-induced risks and volatilities in crop supply

Climate change is intensifying the frequency and severity of extreme events, posing challenges to food security. Corn, a staple crop for billions, is particularly vulnerable to heat stress, a primary driver of yield variability. While many studies have examined climate impact on average corn yields, little attention has been given to the climate impact on production volatility. This study investigates the future volatility and risks associated with global corn supply under climate change, evaluating the potential benefits of two key adaptation strategies: irrigation and market integration. A statistical model is employed to estimate corn yield response to heat stress and utilize NEX-GDDP-CMIP6 climate data to project future production volatility and risks of substantial yield losses. Three metrics are introduced to quantify these risks: Sigma (σ), the standard deviation of year-on-year yield change, which reflects overall yield volatility; Rho (ρ), the risk of substantial loss, defined as the probability of yield falling below a critical threshold; and Beta (β), a relative risk coefficient that captures the volatility of a region's corn production compared to the globally integrated market. The analysis reveals a concerning trend of increasing year-on-year yield volatility (σ) across most regions and climate models. This volatility increase is significant for key corn-producing regions like Brazil and the United States. While irrigated corn production exhibits a smaller rise in volatility, suggesting irrigation as a potential buffer against climate change impacts, it is not a sustainable option as it can cause groundwater depletion. On the other hand, global market integration reduces overall volatility and market risks significantly with less sustainability concerns. Furthermore, these findings highlight the importance of a multidimensional approach to adaptation in the food sector. While irrigation can benefit individual farmers, promoting global market integration offers a broader solution for fostering resilience and sustainability across the entire food system.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Integrating data types to estimate spatial patterns of avian migration across the Western Hemisphere

For many avian species, spatial migration patterns remain largely undescribed, especially across hemispheric extents. Recent advancements in tracking technologies and high-resolution species distribution models (i.e., eBird Status and Trends products) provide new insights into migratory bird movements and offer a promising opportunity for integrating independent data sources to describe avian migration. Here, we present a three-stage modeling framework for estimating spatial patterns of avian migration. First, we integrate tracking and band re-encounter data to quantify migratory connectivity, defined as the relative proportions of individuals migrating between breeding and nonbreeding regions. Next, we use estimated connectivity proportions along with eBird occurrence probabilities to produce probabilistic least-cost path (LCP) indices. In a final step, we use generalized additive mixed models (GAMMs) both to evaluate the ability of LCP indices to accurately predict (i.e., as a covariate) observed locations derived from tracking and band re-encounter data sets versus pseudo-absence locations during migratory periods and to create a fully integrated (i.e., eBird occurrence, LCP, and tracking/band re-encounter data) spatial prediction index for mapping species-specific seasonal migrations. To illustrate this approach, we apply this framework to describe seasonal migrations of 12 bird species across the Western Hemisphere during pre- and postbreeding migratory periods (i.e., spring and fall, respectively). We found that including LCP indices with eBird occurrence in GAMMs generally improved the ability to accurately predict observed migratory locations compared to models with eBird occurrence alone. Using three performance metrics, the eBird + LCP model demonstrated equivalent or superior fit relative to the eBird-only model for 22 of 24 species–season GAMMs. In particular, the integrated index filled in spatial gaps for species with over-water movements and those that migrated over land where there were few eBird sightings and, thus, low predictive ability of eBird occurrence probabilities (e.g., Amazonian rainforest in South America). This methodology of combining individual-based seasonal movement data with temporally dynamic species distribution models provides a comprehensive approach to integrating multiple data types to describe broad-scale spatial patterns of animal movement. Further development and customization of this approach will continue to advance knowledge about the full annual cycle and conservation of migratory birds.

59 BASIC BIOLOGICAL SCIENCES↗

A machine learning approach to galaxy properties: joint redshift–stellar mass probability distributions with Random Forest

We demonstrate that highly accurate joint redshift–stellar mass probability distribution functions (PDFs) can be obtained using the Random Forest (RF) machine learning (ML) algorithm, even with few photometric bands available. As an example, we use the Dark Energy Survey (DES), combined with the COSMOS2015 catalogue for redshifts and stellar masses. We build two ML models: one containing deep photometry in the griz bands, and the second reflecting the photometric scatter present in the main DES survey, with carefully constructed representative training data in each case. We validate our joint PDFs for 10 699 test galaxies by utilizing the copula probability integral transform and the Kendall distribution function, and their univariate counterparts to validate the marginals. Benchmarked against a basic set-up of the template-fitting code bagpipes, our ML-based method outperforms template fitting on all of our predefined performance metrics. In addition to accuracy, the RF is extremely fast, able to compute joint PDFs for a million galaxies in just under 6 min with consumer computer hardware. Such speed enables PDFs to be derived in real time within analysis codes, solving potential storage issues. As part of this work we have developed galpro 1, a highly intuitive and efficient python package to rapidly generate multivariate PDFs on-the-fly. galpro is documented and available for researchers to use in their cosmology and galaxy evolution studies.

79 ASTRONOMY AND ASTROPHYSICS↗

Model Gap Quantification and Evaluation

In the real world, model gaps always exist because models cannot perfectly match the objective physical plants. Model gaps reflect the integrity of models, which is vital for model validation and calibration. This letter proposes a novel approach for model gap quantification and evaluation. First, a comprehensive metric is developed to quantify dynamic model gaps. Next, the model gaps are evaluated from a panoramic view of the probability distribution of the comprehensive metric for multiple scenarios. Finally, we demonstrate the proposed quantification and evaluation approach through synchronous machine models.

Wang, Shaobu↗

Computational Modeling of Graphite Degradation due to Molten Salt Infiltration and Wear

Molten-salt reactors (MSRs) represent a promising next-generation reactor design, with graphite serving as a moderator and/or reflector in several designs. However, due to limited experimental data and operational experience, a technical understanding of the structural integrity of graphite in molten salt environments remains incomplete. This report presents a modeling-based evaluation of graphite degradation in MSR environments, focusing on the effects of salt infiltration in fuel salt-based designs and surface wear in pebble bed reactor designs. The objective of this study is to enhance understanding of the structural integrity challenges posed by these degradation mechanisms and to provide a framework for assessing graphite behavior in MSRs. The first part of the report investigates the phenomenon of molten salt infiltration into graphite. This infiltration occurs when molten salt permeates the interconnected pore structure of the graphite moderator, driven by factors such as pressure differentials and the physical properties of both the salt and graphite. The infiltration process is influenced by characteristics of the pore structure, viscosity of the molten salt, and the interfacial energies between the graphite, salt, and the atmosphere within the graphite pore. Utilizing a coupled multiphysics modeling approach with Grizzly software, the study evaluates the stress induced by internal heat sources due to infiltration, which can lead to structural concerns. This evaluation is crucial for understanding how infiltration affects the mechanical integrity of graphite components in MSRs. The study considers the Molten-Salt Reactor Experiment (MSRE) graphite stringer geometry due to the availability of relevant data. Through detailed finite element analysis, the study examines stress distributions at varying infiltration percentages, revealing that stress levels increase with higher amounts of infiltration. Rare-event simulations, using the parallel subset simulation (PSS) framework, further quantify the failure probabilities under input uncertainties, with a user-specified failure metric. The PSS framework also identifies critical input parameters that significantly affect the stress values, including infiltration amount, thermal conductivity, and power density. Additionally, considering realistic reactor scenarios, the analysis was performed to account for the combined effects of radiation and infiltration, and modeling strategies on how to analyze new reactor designs or new graphite grades are discussed. The second part of the report focuses on wear mechanisms in pebble bed-based MSRs. As graphite fuel pebbles interact with the graphite reflector block, wear can result in material loss and the formation of surface defects, which may act as stress concentrators. A similar multiphysics modeling framework is employed to assess the impact of wear on the structural integrity of graphite components. This study considers a generic fluoride-cooled high-temperature reactor (gFHR) design due to the availability of comprehensive data. Worst-case scenario dimensions of the reflector blocks were analyzed under thermal and radiation conditions. Subsequently, wear in the form of idealized pits and grooves is modeled on the inner surface of the graphite block, with the maximum stress from previous simulations. The simulations show that groove-type defects are more detrimental than pits, leading to higher stress concentrations. Considering worst-case simulation scenarios and experimental wear rates, it was determined that the formation of a surface defect critical enough to affect the stress may not be possible in a gFHR design. Overall, the findings of this research contribute to the development of robust modeling tools for predicting graphite behavior under various operational conditions in MSRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Powered By ERAD [Slides]

Energy Resilience Analysis for Distribution Power System (ERAD) is a free, open-source Python toolkit for estimating the energy and service impacts of hazards like earthquakes and flooding. It uses a graph-based approach to capture high resolution connectivity among the grid, critical services, and customers and rapidly compute household level metrics and aggregated statistics across large distribution systems. It uses asset fragility curves that relate hazard severity to survival probability for power system equipment including cables, transformers, substations, etc. The tool is designed to be modular and extensible, allowing it to interface with third-party hazard simulators and integrate into broader resilience analysis workflows. ERAD enables researchers, students, communities, distribution utilities, and other stakeholders to understand hazard impacts and evaluate the effectiveness of different programs to improve energy resilience. The webinar was hosted by NLR researcher Aadil Latif.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Open Call LDRD: Physically Informed Autoencoders for Galactic Redshift Regression

Physical constraints have been suggested to make neural network models more generalizable, act scientifically plausible, and be more data-efficient over unconstrained baselines. In this report, we present preliminary work on evaluating the effects of adding soft physical constraints to computer vision neural networks trained to estimate the conditional density of redshift on input galaxy images for the Sloan Digital Sky Survey. We introduce physically motivated soft constraint terms that are not implemented with differential or integral operators. We frame this work as a simple ablation study where the effect of including soft physical constraints is compared to an unconstrained baseline. We compare networks using standard point estimate metrics for photometric redshift estimation, as well as metrics to evaluate how faithful our conditional density estimate represents the probability over the ensemble of our test dataset. We find no evidence that the implemented soft physical constraints are more effective regularizers than augmentation.

97 MATHEMATICS AND COMPUTING↗

High-throughput validation of phase formability and simulation accuracy of Cantor alloys

High-throughput methods enable accelerated discovery of novel materials in complex systems such as high-entropy alloys, which exhibit intricate phase stability across vast compositional spaces. Computational approaches, including Density Functional Theory (DFT) and calculation of phase diagrams (CALPHAD), facilitate screening of phase formability as a function of composition and temperature. However, the integration of computational predictions with experimental validation remains challenging in high-throughput studies. In this work, we introduce a quantitative confidence metric to assess the agreement between predictions and experimental observations, providing a quantitative measure of the confidence of machine learning models trained on either DFT or CALPHAD input in accounting for experimental evidence. The experimental dataset was generated via high-throughput in-situ synchrotron X-ray diffraction on compositionally varied FeNiMnCr alloy libraries, heated from room temperature to ~1000 °C. Agreement between the observed and predicted phases was evaluated using either temperature-independent phase classification or a model that incorporates a temperature-dependent probability of phase formation. This integrated approach demonstrates where strong overall agreement between computation and experiment exists, while also identifying key discrepancies, particularly in FCC/BCC predictions at Mn-rich regions to inform future model refinement.

36 - MATERIALS SCIENCE↗

Data-Driven Computation of Probabilistic Marching Cubes for Efficient Visualization of Level-Set Uncertainty

Uncertainty visualization is an important emerging research area. Being able to visualize data uncertainty can help scientists improve trust in analysis and decision-making. However, visualizing uncertainty can add computational overhead, which can hinder the efficiency of analysis. In this paper, we propose novel data-driven techniques to reduce the computational requirements of the probabilistic marching cubes (PMC) algorithm. PMC is an uncertainty visualization technique that studies how uncertainty in data affects level-set positions. However, the algorithm relies on expensive Monte Carlo (MC) sampling for the multivariate Gaussian uncertainty model because no closed-form solution exists for the integration of multivariate Gaussian. In this work, we propose the eigenvalue decomposition and adaptive probability model techniques that reduce the amount of MC sampling in the original PMC algorithm and hence speed up the computations. Our proposed methods produce results that show negligible differences compared with the original PMC algorithm demonstrated through metrics, including root mean squared error, maximum error, and difference images. We demonstrate the performance and accuracy evaluations of our data-driven methods through experiments on synthetic and real datasets.

Athawale, Tushar↗