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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An uncertainty quantification method relevant to material test reactors

Within material test reactor calculations, energy dependent flux and reaction rate uncertainties are typically not quantified when performing as-run analyses to determine the neutron field experienced by the experiment. When high fidelity Monte-Carlo codes are used in such analyses, straight forward methods to calculate output uncertainties are not available, instead expert opinion is used to postulate computational uncertainties. New methods to propagate uncertainties through these high fidelity simulations are available when sufficient computational power is available. A tool is developed here for sampling any part of an MCNP input from random distributions to determine output uncertainties based on those inputs. Another tool is developed to sample nuclear data cross-section in ACE format using multi-group nuclear data covariances. The Total Monte-Carlo Method and Gesellschaft für Anlagen-und Reaktorsicherheit method (GRS) are implemented and compared to one another as well as MCNP sensitivity and uncertainty calculations. The methods were applied to the Godiva critical sphere k-eigenvalue, the UAM pin-cell benchmark energy dependent flux and reaction rates, and the Advanced Test Reactor energy dependent flux within an experimental location. Furthermore, the two methods agree well, with GRS allowing for an order of magnitude speedup for reaction rate uncertainty calculations and several orders of magnitude for eigenvalue uncertainty calculations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Development and application of two-step uncertainty propagation and sensitivity analysis methodology for fast reactor safety analysis

Uncertainty quantification (UQ) in nuclear reactors for transients is directly linked with safety assessment through the cross-sections uncertainties, provided as a covariance matrix, which are propagated through the reactor system to output of interest pertaining to reactor safety, such as peak temperatures in fuel/clad/coolant. Using a two-step approach, uncertainties are first quantified and propagated from basic input variables (such as reaction cross-sections) to intermediate quantities (such as reactivity feedback coefficients) through lattice level calculations. Uncertainties of intermediate quantities (from the first step) are then propagated through the system transient calculations, in the second step, to obtain uncertainties on reactor safety output parameters of interest. The scope of this work consists of Uncertainty Quantification & Propagation of nuclear data uncertainties that are highly correlated through unprotected transient overpower and unprotected loss of flow to assess their impact on core safety parameters. This two-step approach in the presence of covariance renders the sensitivity analysis very challenging. In fact, usually the sensitivity analysis is restricted to each step, which limits its application since the sensitivities between the system output quantities and the basic input variables are difficult to obtain. Here, in this work, we address this issue by proposing a simple, general methodology to combine the sensitivity indices obtained in each step by assuming the model behavior being linear. For the first step Generalized Perturbation theory based indices are used while in the second step the recently studied Johnson indices. The uncertainty quantification and sensitivity methodologies discussed here are demonstrated on a generic LFR design which is based on the 500 MWth demonstration Lead-cooled fast reactor (DLFR) using oxide fuel, developed by Westinghouse Electric Company (WEC).

42 - ENGINEERING↗
DOE OSTI2022

Network Uncertainty Quantification for Analysis of Multi-Component Systems

To impact physical mechanical system design decisions and realize the full promise of high-fidelity computational tools, simulation results must be integrated at the earliest stages of the design process. This is particularly challenging when dealing with uncertainty and optimizing for system-level performance metrics, as full-system models (often notoriously expensive and time-consuming to develop) are generally required to propagate uncertainties to system-level quantities of interest. Methods for propagating parameter and boundary condition uncertainty in networks of interconnected components hold promise for enabling design under uncertainty in real-world applications. These methods avoid the need for time consuming mesh generation of full-system geometries when changes are made to components or subassemblies. Additionally, they explicitly tie full-system model predictions to component/subassembly validation data which is valuable for qualification. These methods work by leveraging the fact that many engineered systems are inherently modular, being comprised of a hierarchy of components and subassemblies that are individually modified or replaced to define new system designs. By doing so, these methods enable rapid model development and the incorporation of uncertainty quantification earlier in the design process. The resulting formulation of the uncertainty propagation problem is iterative. We express the system model as a network of interconnected component models, which exchange solution information at component boundaries. We present a pair of approaches for propagating uncertainty in this type of decomposed system and provide implementations in the form of an open-source software library. We demonstrate these tools on a variety of applications and demonstrate the impact of problem-specific details on the performance and accuracy of the resulting UQ analysis. This work represents the most comprehensive investigation of these network uncertainty propagation methods to date.

42 ENGINEERING↗
DOE OSTI2023

Uncertainty quantification of bank vegetation impacts on the flood flow field in the American River, California, using large‐eddy simulations

Bank vegetation plays a key role in both hydrodynamics and morphodynamics of natural rivers; however, these effects are often unaccounted for in the computational flow dynamics of natural waterways. Recent studies using the large‐eddy simulation (LES), however, have attempted to gain insights into the impacts of bank vegetation on the mean flow field of the natural rivers using a vegetation model, which applies a sink term to the momentum equations of motion. This approach accounts for the effects of the vegetation and provides a practical approach to account for the complex patches of bank vegetation in large‐scale rivers. To implement the vegetation model, a drag coefficient reflecting the overall resistance of vegetal structures to the flow is needed, but due to the lack of calibrated data and range of size, density and type of vegetation, this parameter can be a significant source of uncertainty in the model results. Here, in this study, we use uncertainty quantification (UQ) to investigate the hydrodynamics and bed shear results when a bank vegetation is incorporated in an LES model. To this end, we used the polynomial chaos expansion and Monte Carlo sampling techniques to determine the uncertainties associated with the drag coefficient in the vegetation model and from uncertainties in the bed roughness and inflow discharge. The UQ analysis provided spatially varying confidence levels for the spanwise and vertical distribution of velocity magnitude and for the bed shear stress distributions. In addition, Sobol indices were computed to indicate the relative influence that each parameter had on the overall uncertainty. In general, it was found that uncertainty in flow discharge was the dominant source of uncertainty; however, the drag coefficient in the vegetation model and the bed roughness parameter also made significant contribution to the uncertainty near the banks and bed, respectively.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Updates to the Regional Seismic Travel Time (RSTT) Model: 2. Path-dependent Travel-time Uncertainty

Abstract The regional seismic travel time (RSTT) model and software were developed to improve travel-time prediction accuracy by accounting for three-dimensional crust and upper mantle structure. Travel-time uncertainty estimates are used in the process of associating seismic phases to events and to accurately calculate location uncertainty bounds (i.e. event location error ellipses). We improve on the current distance-dependent uncertainty parameterization for RSTT using a random effects model to estimate slowness (inverse velocity) uncertainty as a mean squared error for each model parameter. The random effects model separates the error between observed slowness and model predicted slowness into bias and random components. The path-specific travel-time uncertainty is calculated by integrating these mean squared errors along a seismic-phase ray path. We demonstrate that event location error ellipses computed for a 90% coverage ellipse metric (used by the Comprehensive Nuclear-Test-Ban Treaty Organization International Data Centre (IDC)), and using the path-specific travel-time uncertainty approach, are more representative (median 82.5% ellipse percentage) of true location error than error ellipses computed using distance-dependent travel-time uncertainties (median 70.1%). We also demonstrate measurable improvement in location uncertainties using the RSTT method compared to the current station correction approach used at the IDC (median 74.3% coverage ellipse).

58 GEOSCIENCES↗
DOE OSTI2021

Sensitive parameter identification and uncertainty quantification for the stability of pipeline conveying fluid

In this study, several uncertainty quantification and sensitivity analysis methods are used to determine the most sensitive geometric and material input parameters of a cantilevered pipeline conveying fluid when uncertainty is introduced to the system at the onset of instability. The full nonlinear equations of motion are modeled using the extended Hamilton’s principle and then discretized using Galerkin’s method. A parametric study is first performed, and the Morris elementary effects are calculated to obtain a preliminary understanding of how the onset speed changes when each parameter is introduced to a ± 5% uncertainty. Then, four different input uncertainty distributions, mainly, uniform and Gaussian distribution, are chosen to investigate how input distributions affect uncertainty in the output. A convergence analysis is used to determine the number of samples needed to maintain simulation accuracy while saving the most computational time. Then, Monte Carlo simulations are run, and the output distributions for each input distribution at ± 1%, ± 3% and ± 5% input uncertainty range are found and discussed. Additionally, the Pearson correlation coefficients are evaluated for different uncertainty ranges. A final Monte Carlo study is performed in which single parameters are held constant while all others still have uncertainty. Overall, the flow speed at the onset of instability is the most sensitive to changes in the outer diameter of the pipe.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Propagation of Noise Uncertainty Through Virtual Strain Gauge Formulations for 2D Digital Image Correlation

The effect of displacement uncertainty is examined on 2-dimensional strain, calculated using linear surfaces fitted to the displacement field. A classical engineering error propagation method is used to calculate uncertainty in Green-Lagrangian strain calculations. The derived uncertainty is compared to a Monte Carlo simulation and discrepancies under 2% are seen between these two methods. The effect of virtual strain gauge size, displacement uncertainty, and boundaries on the region of interest on the strain uncertainty are considered. Here, an exponential decay relationship is observed between strain uncertainty and virtual strain gauge size, while a linear relationship is seen between strain and displacement uncertainty. For boundaries in the region of interest, strain uncertainty is affected by the reduced number of points available to perform the regression.

42 ENGINEERING↗
DOE OSTI2025

Denoising Autoencoder for Reconstructing Sensor Observation Data and Predicting Evapotranspiration: Noisy and Missing Values Repair and Uncertainty Quantification

Abstract Machine learning (ML) methods applied in scientific research often deal with interrelated features in high‐dimensional data. Reducing data noise and redundancy is needed to increase prediction accuracy and efficiency especially when dealing with data from field sensors. We explored an unsupervised learning method, the denoising autoencoder (DAE), to extract the underlying data structure from noisy raw data in the context of predicting hydrologic quantities from multiple field sensors. These sensors have intrinsic instrumental noise and occasional malfunctions that cause missing values. Our DAE neural network reconstructed meteorological sensor data containing noise and missing values to predict evapotranspiration in a mountainous watershed. The DAE reconstructed the sensor variables with a mean coefficient of determination value of 0.77 across 15 dimensions representing individual sensors. It reduced variance and bias uncertainties compared to a classical autoencoder model. The reconstruction quality varied across dimensions depending on their cross‐correlation and alignment with the underlying data structure. Uncertainties arising from the model structure were overall higher than those resulting from data corruption. We attached the DAE structure to a downstream ET‐prediction neural network in three formats and achieved reasonably accurate ET predictions . The use of the DAE notably reduced variance uncertainty in ET prediction. However, excessive variance reduction may be accompanied by an increase in bias due to the intrinsic bias‐variance tradeoff. Our method of evaluating and reducing uncertainties in aggregated data from different sources can be used to improve predictive models, process understanding, and uncertainty quantification for better water resource management. Plain Language Summary We present a machine learning method, namely the denoising autoencoder, which reduces the effects of data noise and missing values typically present in scientific data sets collected through sensor measurements. This method selects the most relevant information from noisy raw data collected by the instruments and fills in missing values. To demonstrate the effectiveness of our method, we applied it to predict evapotranspiration, a hydrologic variable that represents the water moved from the land surface to the atmosphere through a combination of evaporation and plant water use (transpiration). We also used a random sampling technique (the Monte Carlo method) to compare the uncertainty in the predictions when using the raw and noisy data versus the reconstructed data. The denoising process produced more accurate predictions of evapotranspiration with less uncertainty. Improved predictions of evapotranspiration can lead to a better understanding and accounting of water budgets. This ML approach is broadly suitable for a wide variety of applications that involve noisy sensor data with missing values. Key Points We used a denoising autoencoder (DAE) neural network to reduce noise in meteorological and soil sensor observations by on average We used Monte Carlo sampling to estimate the bias and variance of all model outputs, including uncertainty sources from data and the model We attached the DAE component to a downstream neural network to predict ET with the variance reduced by , compared to that without the DAE

denoising autoencoder↗
DOE OSTI2023

Visualization and Decision Making Design Under Uncertainty

Uncertainty is an important aspect to data understanding. Without awareness of the variability, error, or reliability of a dataset, the ability to make decisions on that data is limited. However, practices around uncertainty visualization remain domain-specific, rooted in convention, and in many instances, absent entirely. Part of the reason for this may be a lack of established guidelines for navigating difficult choices of when uncertainty should be added, how to visualize uncertainty, and how to evaluate its effectiveness. Unsurprisingly, the inclusion of uncertainty into visualizations is a major challenge to visualization. As work concerned with uncertainty visualization grows, it has become clear that simple visual additions of uncertainty information to traditional visualization methods do not appropriately convey the meaning of the uncertainty, pose many perceptual challenges, and, in the worst case, can lead a viewer to a completely wrong understanding of the data. These challenges are the driving motivator for this special issue.

data models↗
DOE OSTI2026

MAGIC: M arching Cubes Isosurface Uncertainty Visualization for G auss i an Uncertain Data With Spatial C orrelation

Here, in this paper, we study the propagation of data uncertainty through the marching cubes algorithm for isosurface visualization for correlated uncertain data. Consideration of correlation has been shown paramount for avoiding errors in uncertainty quantification and visualization in multiple prior studies. Although the problem of isosurface uncertainty with spatial data correlation has been previously addressed, there are two major limitations to prior treatments. First, there are no analytical formulations for uncertainty quantification of isosurfaces when the data uncertainty is characterized by a Gaussian distribution with spatial correlation. Second, as a consequence of the lack of analytical formulations,existing techniques resort to a Monte Carlo sampling approach, which is expensive and difficult to integrate into visualization tools. To address these limitations, we present a closed-form framework to efficiently derive uncertainty in marching cubes level-sets for Gaussian uncertain data with spatial correlation (MAGIC). To derive closed-form solutions, we leverage the Hinkley's derivation on the ratio of Gaussian distributions. With our analytical framework, we achieve a significant speed-up and enhanced accuracy of uncertainty quantification over classical Monte Carlo methods. We further accelerate our analytical solutions using many-core processors to achieve speed-ups up to 585× and integrability with production visualization tools for broader impact. We demonstrate the effectiveness of our correlation-aware uncertainty framework through experiments on meteorology, urban flow, and astrophysics simulation datasets.

Gaussian↗
DOE OSTI2022

Characterization and Valuation of the Uncertainty of Calibrated Parameters in Microsimulation Decision Models

We evaluated the implications of different approaches to characterize the uncertainty of calibrated parameters of microsimulation decision models (DMs) and quantified the value of such uncertainty in decision making. We calibrated the natural history model of CRC to simulated epidemiological data with different degrees of uncertainty and obtained the joint posterior distribution of the parameters using a Bayesian approach. We conducted a probabilistic sensitivity analysis (PSA) on all the model parameters with different characterizations of the uncertainty of the calibrated parameters. We estimated the value of uncertainty of the various characterizations with a value of information analysis. We conducted all analyses using high-performance computing resources running the Extreme-scale Model Exploration with Swift (EMEWS) framework. The posterior distribution had a high correlation among some parameters. The parameters of the Weibull hazard function for the age of onset of adenomas had the highest posterior correlation of -0.958. When comparing full posterior distributions and the maximum-a-posteriori estimate of the calibrated parameters, there is little difference in the spread of the distribution of the CEA outcomes with a similar expected value of perfect information (EVPI) of $\$$653 and $\$$685, respectively, at a willingness-to-pay (WTP) threshold of $\$$66,000 per quality-adjusted life year (QALY). Ignoring correlation on the calibrated parameters’ posterior distribution produced the broadest distribution of CEA outcomes and the highest EVPI of $\$$809 at the same WTP threshold. Different characterizations of the uncertainty of calibrated parameters affect the expected value of eliminating parametric uncertainty on the CEA. Ignoring inherent correlation among calibrated parameters on a PSA overestimates the value of uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Combined Data and Deep Learning Model Uncertainties: An Application to the Measurement of Solid Fuel Regression Rate

In complex physical process characterization, such as the measurement of the regression rate for solid hybrid rocket fuels, where both the observation data and the model used have uncertainties originating from multiple sources, combining these in a systematic way for quantities of interest (QoI) remains a challenge. In this paper, we present a forward propagation uncertainty quantification (UQ) process to produce a probabilistic distribution for the observed regression rate r. We characterized two input data uncertainty sources from the experiment (the distortion from the camera U c and the non-zero-angle fuel placement U Y ), the prediction and model form uncertainty from the deep neural network (U m ), as well as the variability from the manually segmented images used for training it (U s ). Here, we conducted seven case studies on combinations of these uncertainty sources with the model form uncertainty. The main contribution of this paper is the investigation and inclusion of the experimental image data uncertainties involved, and how to include them in a workflow when the QoI is the result of multiple sequential processes.

42 ENGINEERING↗
DOE OSTI2022

Investigating uncertainties in human adaptation and their impacts on water scarcity in the Colorado river Basin, United States

The Colorado River Basin (CRB) supports the water supply for seven states and forty million people in the Western United States (US) and has been suffering an extensive drought for more than two decades. As climate change continues to reshape water resources distribution in the CRB, its impact can differ in intensity and location, resulting in variations in human adaptation behaviors. The feedback from human systems in response to the environmental changes and the associated uncertainty is critical to water resources management, especially for water-stressed basins. This paper investigates how human adaptation affects water scarcity uncertainty in the CRB and highlights the uncertainties in human behavior modeling. Our focus is on agricultural water consumption, as approximately 80% of the water consumption in the CRB is used in agriculture. We adopted a coupled agent-based and water resources modeling approach for exploring human-water system dynamics, in which an agent is a human behavior model that simulates a farmer’s water consumption decisions. We examined uncertainties at the system, agent, and parameter levels through uncertainty, clustering, and sensitivity analyses. The uncertainty analysis results suggest that the CRB water system may experience 13 to 30 years of water shortage during the 2019–2060 simulation period, depending on the paths of farmers’ adaptation. The clustering analysis identified three decision-making classes: bold, prudent, and forward-looking, and quantified the probabilities of an agent belonging to each class. The sensitivity analysis results indicated agents whose decision-making models require further investigation and the parameters with the higher uncertainty reduction potentials. Here, by conducting numerical experiments with the coupled model, this paper presents quantitative and qualitative information about farmers’ adaptation, water scarcity uncertainties, and future research directions for improving human behavior modeling.

Agent-based modeling↗
DOE OSTI2025

Identifying high-impact and high-uncertainty parameters in MiniFuel model predictions

The MiniFuel irradiation platform at Oak Ridge National Laboratory's High Flux Isotope Reactor (HFIR) is a flexible, high-throughput separate effects test capability. Finite element thermal models are relied upon to design MiniFuel experiments and to achieve experimental objectives. Recent reports show good agreement in the model prediction of target fuel temperatures, but as the capability of the experiments is extended to higher temperatures, the uncertainty in the model predictions must be quantified. To that end, high-impact, high-uncertainty parameters that contribute the most uncertainty to the model are identified. The uncertainty quantification was accomplished through a series of screening and sensitivity analyses. The first analysis utilizes the method of Morris to perform a computationally efficient preliminary screening that considers uncertainty in a large number of the model inputs. The most important parameters identified in the Morris screening study were then considered in a Sobol sensitivity analysis that more robustly ranks and quantifies the uncertainty associated with each parameter. From these analyses, it was determined that thermal contact conductance between components is the parameter that contributes the highest uncertainty. The estimated uncertainty of the MiniFuel model fuel temperature predictions is ±80 °C in the removable beryllium and ±40 °C in the vertical experiment facilities. In conclusion, the framework established by the series of sensitivity analyses presented herein could easily be adapted to fit the needs of accelerated fuel qualification processes.

Fuel, Irradiation↗
DOE OSTI2021

Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments

In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.

42 ENGINEERING↗
DOE OSTI2023

Urban Flood Modeling: Uncertainty Quantification and Physics‐Informed Gaussian Processes Regression Forecasting

Abstract Estimating uncertainty in flood model predictions is important for many applications, including risk assessment and flood forecasting. We focus on uncertainty in physics‐based urban flooding models. We consider the effects of the model's complexity and uncertainty in key input parameters. The effect of rainfall intensity on the uncertainty in water depth predictions is also studied. As a test study, we choose the Interconnected Channel and Pond Routing (ICPR) model of a part of the city of Minneapolis. The uncertainty in the ICPR model's predictions of the floodwater depth is quantified in terms of the ensemble variance using the multilevel Monte Carlo (MC) simulation method. Our results show that uncertainties in the studied domain are highly localized. Model simplifications, such as disregarding the groundwater flow, lead to overly confident predictions, that is, predictions that are both less accurate and uncertain than those of the more complex model. We find that for the same number of uncertain parameters, increasing the model resolution reduces uncertainty in the model predictions (and increases the MC method's computational cost). We employ the multilevel MC method to reduce the cost of estimating uncertainty in a high‐resolution ICPR model. Finally, we use the ensemble estimates of the mean and covariance of the flood depth for real‐time flood depth forecasting using the physics‐informed Gaussian process regression method. We show that even with few measurements, the proposed framework results in a more accurate forecast than that provided by the mean prediction of the ICPR model.

Kohanpur, Amir H.↗
DOE OSTI2025

Combined Meteorological and Hydrologic Uncertainties Shape Projections of Future Soil Moisture in the Eastern United States

Physical hazards pose risks to many critical systems. Designing adaptive measures to mitigate these risks is challenging due to large uncertainties in modeling future hazards and the associated sectoral responses. Here, we help address this challenge in a hydrologic context by examining the combined role of meteorological forcing and hydrologic parameter uncertainties in shaping projections of future soil moisture. By encoding a simple conceptual water balance model in a differentiable programming framework, we facilitate fast runtimes and an efficient calibration, enabling an improved uncertainty analysis. We characterize uncertainty in model parameters by calibrating against different target data sets and by using several loss functions. We then convolve the resulting parameter ensemble with a set of Earth system model projections to produce a large ensemble (2,340 members) of daily soil moisture simulations. Focusing on the eastern United States, we find that most ensemble members project a drying of soils across the region, although some simulate wetter conditions throughout this century. Our ensemble shows an increase in the frequency and intensity of dry extremes while there is less agreement for wet extremes. We conduct sensitivity analyses on several soil moisture signatures to measure the relative influence of meteorological and hydrologic uncertainties across space and time. Both meteorological and hydrologic factors contribute consistently to uncertainty surrounding long-term trends, while changes to both wet and dry soil extremes are typically more sensitive to hydrologic parameter uncertainty. Our results underscore the need to account for varied sources of uncertainty when developing long-term hydrometeorological projections.

Lafferty, David C. [University of Illinois Urbana‐↗
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↗