Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probabilistic”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. Here, in this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.

Dirichlet-to-Neumann map↗
DOE OSTI2025

A Probabilistic Reasoner Based on Bayes Risk for Damage Detection in Structural Systems

Structural health monitoring (SHM) systems are used to inform operation of structural systems subject to loads and environments that may affect their integrity. SHM systems rely on continuous monitoring of the structure to determine its health state. These systems are often coupled with a model of the deployed structure to determine the consequences of changes in the system by forecasting the response to future states. These models, which may be thought of as digital twins, need to be updated to reflect the latest state of the structural system. This work makes use of an uncertainty-aware machine learning model that enforces distance preservation of the original input space to determine deviations from the training data input space distributions. This workflow enables domain shift detection to determine whether damage is present in the structure. The uncertainty metrics generated by this network are then used in a Bayes risk framework to design an optimal damage detector given cost and risk considerations. The approach is demonstrated on a computational example with simulated damage.

Najera-Flores, David [ATA Engineering, Inc.]↗
DOE OSTI2024

A Prefire Approach for Probabilistic Assessments of Postfire Debris-Flow Inundation

Increases in wildfire activity and rainfall intensification are driving more postfire debris flows (PFDF) in many regions around the world. PFDFs are most common in the first postfire year and may even occur before a fire is fully controlled. This underscores the importance of assessing postfire hazards before a fire starts. Evaluation of PFDF hazards prior to fire can help strategize interventions lessening the negative effects of future fires. However, debris-flow runout and inundation analyses are not routine in PFDF hazard assessments, partially due to time constraints and substantial uncertainties in boundary conditions. Here, we propose a prefire PFDF inundation assessment framework using a debris-flow runout model based on the Herschel-Bulkley (HB) rheology (HEC-RAS v6.1). We constrain model inputs and parameters using Bayesian posterior analysis, rainfall-runoff simulations, and a debris-flow volume model. We use observations from recent PFDF incidents in northern Arizona, USA, to calibrate model components and then apply our prefire inundation assessment framework in a nearby unburned area. Specifically, we (a) identify yield stress as the most influential factor on inundation extent and arrival time in a HB model, (b) establish posterior distributions for model parameters suitable for forward modeling by leveraging uncertainties in field observations, and (c) implement a predictive forward analysis in an area that has not burned recently to evaluate PFDF inundation under several future fire scenarios. This study improves our ability to assess postfire debris-flow hazards before a fire begins and provides guidance for future applications of single-phase rheological models when assessing PFDF hazards.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Probabilistic Error Bounds for Low-Rank Tensor Decompositions Used in Large-Scale Data Analysis Applications (LDRD Final Report)

This report documents a research project on analyzing low-rank tensor models for data analysis that took place at Sandia National Laboratories from October 2023–September 2025. The focus of this work was to extend theoretical frameworks from statistics and probability theory for use with models for scalar, vector, and matrix data to models with tensor, or general multi-dimensional array, data. Through this work, we have provided a new set of tools for bounding errors on low-rank tensor models of both complete and sampled data. The remainder of this report is organized as follows. In Section 1, we describe the proposed work at the start of the project. Section 2 describes the research advances made as part of the project. Other research contributions in the form of conference presentations and software development is provided in Section 3. Workforce development at Sandia and Florida Atlantic University (via a subcontract on this project) is provided in Section 4.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Probabilistic Hazard Assessment for Tornadoes, Straight-Line Wind, and Extreme Precipitation at the Savannah River Site

Recent data sets for three meteorological phenomena with the potential to inflict damage on SRS facilities – tornadoes, straight-line winds, and heavy precipitation – are analyzed using appropriate statistical techniques to estimate the occurrence probabilities for these events in the future. Summaries of the results for DOE-mandated return periods and comparisons to similar calculations performed in 2013 by Werth et al. (W2013) are given. Using tornado statistics for i) the combined states of Georgia and South Carolina, and ii) a 2⁰ square area surrounding SRS, we calculated the probability per year of any location at SRS being struck by a tornado (the ‘strike’ probability) and the probability that any point will experience winds above set thresholds. The strike probability was calculated to be 7.04E-4 (1 chance in 1420) per year and tornadic wind speeds for DOE mandated return periods of 50,000 years (corresponding to wind design category 3 (WDC-3), and 125,000 years (meeting WDC-4) (USDOE, 2016) were estimated to be 132 mph and 147 mph, respectively. By contrast, default tornado wind speeds taken from ANSI/ANS-2.3-2011 are somewhat higher: 161 mph for return periods of 50,000 years and 173 mph every 125,000 years (ANS, 2011). Although the ANS and the SRS evaluation used the same basic model (Ramsdell and Rishel, 2007), the region defined in ANS 2.3 that encompasses the SRS also includes areas of the Great Plains and lower Midwest, regions with much higher occurrence frequencies of strong tornadoes. The SRS straight-line wind values associated with various return periods were calculated by fitting existing wind data to a GEV1 distribution and extrapolating the values for any return period from the tail of that function. For the DOE mandated return periods, we expect straight-line winds of 117 mph every 2500 years (the required WDC-3 standard) and 125 mph every 6250 years (WDC-4) at any point within the SRS. These values are similar to those from the ANS-2.3-2011 report, which has wind speeds of 125mph and 133 mph for return periods of 2500 years and 6250 years, respectively. For extreme precipitation, we compared the fits of two different theoretical extreme-value distributions and applied the one that fit the data best for each of several accumulation periods. The DOE mandated 6-hr accumulated rainfall for return periods of 10,000 years (corresponding to precipitation design category 3 (PDC-3) and 25,000 years (PDC-4) were estimated as 9.1 inches and 10.1 inches, respectively. For the 24-hr rainfall return periods of 10,000 years and 25,000 years, total rainfall estimates were 12.02 inches and 13.17 inches, respectively, higher than comparable values provided in the W2013 report.

54 ENVIRONMENTAL SCIENCES↗