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At least 91 records · Page 5

Intercomparison of Deep Learning Model Architectures for Atmospheric River Prediction

With a rapid surge in the application of machine learning (ML) for a diverse range of tasks in climate science, the present study addresses a challenge for climate scientists when selecting the optimal ML or deep learning (DL) architecture for a given application. In particular, a DL intercomparison study was performed with a focus on forecasting the position of atmospheric rivers (ARs) on short-range time scales (up to 5-day lead times). AR predictions from multiple DL architectures, including various types of convolutional autoencoders and a vision transformer (ViT), were compared against ECMWF ERA5 reanalysis and hindcasts from a global climate model. DL models with similar trainable parameters were trained on ERA5 reanalysis data and AR positions derived from a thresholding algorithm to ensure a fair comparison among the DL models. Each model’s performance and accuracy in forecasting AR location and key input fields within a 5-day window were assessed using metrics of root-mean-square error, anomaly correlation, and mean intersection over union. The ViT architecture outperformed other autoencoder models in most of the metrics. Incorporating additional meteorological fields only yielded slight improvements in forecasting certain fields at longer lead times. The results also suggest that a smaller number of input time steps or smaller number of autoregressive steps can achieve better prediction skills, while also improving the overall computational efficiency. This research offers valuable insights into the strengths and weaknesses of different DL techniques for AR forecasting, hopefully guiding the development of improved models for forecasting this phenomenon.

54 ENVIRONMENTAL SCIENCES↗

Quantifying the effects of mixing state on aerosol optical properties

Abstract. Calculations of the aerosol direct effect on climate rely on simulated aerosol fields. The model representation of aerosol mixing state potentially introduces large uncertainties into these calculations, since the simulated aerosol optical properties are sensitive to mixing state. In this study, we systematically quantified the impact of aerosol mixing state on aerosol optical properties using an ensemble of 1800 aerosol populations from particle-resolved simulations as a basis for Mie calculations for optical properties. Assuming the aerosol to be internally mixed within prescribed size bins caused overestimations of aerosol absorptivity and underestimations of aerosol scattering. Together, these led to errors in the populations' single scattering albedo of up to −22.3 % with a median of −0.9 %. The mixing state metric χ proved useful in relating errors in the volume absorption coefficient, the volume scattering coefficient and the single scattering albedo to the degree of internally mixing of the aerosol, with larger errors being associated with more external mixtures. At the same time, a range of errors existed for any given value of χ. We attributed this range to the extent to which the internal mixture assumption distorted the particles' black carbon content and the refractive index of the particle coatings. Both can vary for populations with the same value of χ. These results are further evidence of the important yet complicated role of mixing state in calculating aerosol optical properties.

54 ENVIRONMENTAL SCIENCES↗

Visualization Quality Assessment

Understanding how inaccuracies in visualizations affect users’ perception and understanding of scientific data is hard. Inaccuracies in visualizations are quite common and could arise from a range of sources such as errors in the original dataset arising from compression artifacts, errors in the capturing device, noise during transmission of the data, effects due to the algorithm being used to convert data to visualization images, images generated from neural networks, and sources we have yet to discover. Many image quality assessment metrics have been developed to quantify image errors. However, these are usually focused on “natural images” rather than visualizations of scientific data. Common image quality assessment metrics (IQAs) include MSE, PSNR, perceptual metrics such SSIM, FSIM as well as perceptual metrics using deep learning approaches. However, a critical part of understanding how errors are perceived by humans, and subsequently developing more accurate quality assessment metrics, is through user evaluation studies. The goal of this software is to develop a visualization quality assessment (VQA) process that will enable the generation of VQAs that can be used to quantify errors in scientific data visualizations. The VQA development process will include software to support user evaluation experimental design, analysis of visualization differences against standard quality metrics, and the ability to develop additional VQA metrics specific to scientific visualization images.

Grosset, Andre↗

Deep learning to estimate permeability using geophysical data

Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. Each measurement in both synthetic and field data is standardized by removing the mean and scaling the time-series to unit variance. This pre-processing step is necessary to bring simulation data closer to field observations. Subsurface process models based on hydrogeophysics are used to generate this synthetic data. Training performed on limited simulation data resulted in the DL model over-fitting. An advanced data augmentation based on mixup is implemented to generate additional training samples to overcome this issue. This mixup technique creates weakly labeled (low-fidelity) samples from strongly labeled (high-fidelity) data. The weakly labeled training data is then used to develop DL-enabled inverse models and reduce over-fitting. As both time-lapse ERT (1133048 features/realization) and 3D permeability (585453 features/realization) data samples are from a high-dimensional space, principal component analysis (PCA) is employed to reduce dimensionality. Encoded ERT and encoded permeability are generated using the trained PCA estimators. A deep neural network is then trained to map the encoded ERT to encoded permeability. This mixup training and unsupervised learning allowed us to build a fast and reasonably accurate DL-based inverse model under limited simulation data. Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. Quantitatively, the average mean squared error (in terms of the natural log) on the strongly labeled training, validation, and test datasets is less than 0.5. The R 2 -score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. Finally, an added benefit in terms of computational cost is that the proposed DL-based inverse model is at least O(10 4 ) times faster than running a forward model once it is trained. Data generation, DL model training, and hyperparameter tuning to identify optimal neural network architectures utilized high-performance computing resources while the DL inference is performed on a standard laptop. Approximately, O(10 5 ) processor hours are used for generating data and DL tuning and training. We acknowledge that the data generation and DL model development are expensive. But once a DL model is trained, it can be re-used for inversion rapidly for the given system, with set physics and domain. Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. This computational savings ≈ O(10 5 ) – O(10 7 )) makes the proposed DL-based inverse model attractive for subsurface imaging and real-time ERT monitoring applications due to fast and yet reasonably accurate estimations of permeability field.

58 GEOSCIENCES↗

Blind Modeling Validation Exercises Using the Horizontal Dry Cask Simulator

The U.S. Department of Energy (DOE) established a need to understand the thermal-hydraulic properties of dry storage systems for commercial spent nuclear fuel (SNF) in response to a shift towards the storage of high-burnup (HBU) fuel (> 45 gigawatt days per metric ton of uranium, or GWd/MTU). This shift raises concerns regarding cladding integrity, which faces increased risk at the higher temperatures within spent fuel assemblies present within HBU fuel compared to low-burnup fuel (≤ 45 GWd/MTU). A dry cask simulator (DCS) was built at Sandia National Laboratories (SNL) in Albuquerque, New Mexico to produce validation-quality data that can be used to test the accuracy of the modeling used to predict cladding temperatures. These temperatures are critical to evaluating cladding integrity throughout the storage cycle of commercial spent nuclear fuel. A model validation exercise was previously carried out for the DCS in a vertical configuration. Lessons learned during the previous validation exercise have been applied to a new, blind study using a horizontal dry cask simulator (HDCS). Three modeling institutions – the Nuclear Regulatory Commission (NRC), Pacific Northwest National Laboratory (PNNL), and Empresa Nacional del Uranio, S.A., S.M.E. (ENUSA) – were granted access to the input parameters from the DCS Handbook, SAND2017-13058R, and results from a limited data set from the horizontal BWR dry cask simulator tests reported in the HDCS update report, SAND2019-11688R. With this information, each institution was tasked to calculate peak cladding temperatures and air mass flow rates for ten HDCS test cases. Axial as well as vertical and horizontal transverse temperature profiles were also calculated. These calculations were done using modeling codes (ANSYS/Fluent, STAR-CCM+, or COBRA-SFS), each with their own unique combination of modeling assumptions and boundary conditions. For this validation study, the ten test cases of the horizontal dry cask simulator were defined by three independent variables – fuel assembly decay heat (0.5 kW, 1 kW, 2.5 W, and 5 kW), internal backfill pressure (100 kPa and 800 kPa), and backfill gas (helium and air). The plots provided in Chapter 3 of this report show the axial, vertical, and horizontal temperature profiles obtained from the dry cask simulator experiments in the horizontal configuration and the corresponding models used to describe the thermal-hydraulic behavior of this system. The tables provided in Chapter 3 illustrate the closeness of fit of the model data to the experiment data through root mean square (RMS) calculations of the error in peak cladding temperatures (PCTs), PCT axial locations, axial temperature profiles, vertical and horizontal temperature profiles at two different axial locations, and air mass flow rates for the ten test cases, normalized by the experimental results. The model results are assigned arbitrary model numbers to retain anonymity. Due to the relatively flat axial temperature profiles, small temperature gradients resulted in large deviations of all models’ PCT axial location from the experimental PCT axial location. When the PCT axial location error is excluded in the calculation of the combined RMS of the normalized errors that considers PCT, the temperature profiles, and the air mass flow rates, the model data fits the experimental data to within 5%. When the vault information is excluded, the model data fits the experimental data to within 2.5%. An error analysis was developed further for one model, using the model and experimental uncertainties in each validation parameter to calculate validation uncertainties. The uncertainties for each parameter were used to define quantifiable validation criteria. For this analysis, the model was considered validated for a given comparison metric if the normalized error in that metric divided by the validation uncertainty was less than or equal to 1. When considering the combined RMS of the normalized errors of all metrics divided by their validation uncertainties, the model was found to have satisfied the criterion for model validation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluating Machine Learning-Based MRI Reconstruction Using Digital Image Quality Phantoms

Quantitative and objective evaluation tools are essential for assessing the performance of machine learning (ML)-based magnetic resonance imaging (MRI) reconstruction methods. However, the commonly used fidelity metrics, such as mean squared error (MSE), structural similarity (SSIM), and peak signal-to-noise ratio (PSNR), often fail to capture fundamental and clinically relevant MR image quality aspects. To address this, we propose evaluation of ML-based MRI reconstruction using digital image quality phantoms and automated evaluation methods. Our phantoms are based upon the American College of Radiology (ACR) large physical phantom but created in k-space to simulate their MR images, and they can vary in object size, signal-to-noise ratio, resolution, and image contrast. Our evaluation pipeline incorporates evaluation metrics of geometric accuracy, intensity uniformity, percentage ghosting, sharpness, signal-to-noise ratio, resolution, and low-contrast detectability. We demonstrate the utility of our proposed pipeline by assessing an example ML-based reconstruction model across various training and testing scenarios. The performance results indicate that training data acquired with a lower undersampling factor and coils of larger anatomical coverage yield a better performing model. The comprehensive and standardized pipeline introduced in this study can help to facilitate a better understanding of the performance and guide future development and advancement of ML-based reconstruction algorithms.

47 OTHER INSTRUMENTATION↗

Scalable Programming Workflows for Validation of Quantum Computers

Hybrid quantum-classical workflows have become standard methods for executing variational algorithms and other quantum simulation techniques, which are key applications for noisy intermediate scale quantum (NISQ) computers. Validating these simulations is an important task which helps gauge the progress of quantum computer development, and classical simulation can serve as a tool to this end. Both exact and more scalable approximate methods with quantifiable error bounds can be used in validation tasks where the applicable metrics include the distance from a calculable ground truth, the quality of an error model fit to data, etc. Here we present a library extension that includes methods for validation of quantum simulations based on scalable hybrid workflows executable on high performance computers. We provide examples that use approximate methods based on tensor networks and stabilizer simulators to bound the error of quantum simulations on NISQ hardware.

Nguyen, Thien↗

PeakQC: A Software Tool for Omics-Agnostic Automated Quality Control of Mass Spectrometry Data

Mass spectrometry is broadly employed to study complex molecular mechanisms in various biological and environmental fields, enabling 'omics' research such as proteomics, metabolomics, and lipidomics. As study cohorts grow larger and more complex with dozens to hundreds of samples, the need for robust quality control (QC) measures through automated software tools becomes paramount to ensure the integrity, high quality, and validity of scientific conclusions from downstream analyses and minimize the waste of resources. Since existing QC tools are mostly dedicated to proteomics, automated solutions supporting metabolomics are needed. To address this need, we developed the software PeakQC, a tool for automated QC of MS data that is independent of omics molecular types (i.e., omics-agnostic). It allows automated extraction and inspection of peak metrics of precursor ions (e.g., errors in mass, retention time, arrival time) and supports various instrumentations and acquisition types, from infusion experiments or using liquid chromatography and/or ion mobility spectrometry front-end separations and with/without fragmentation spectra from data-dependent or independent acquisition analyses. Diagnostic plots for fragmentation spectra are also generated. Here, in this paper, we describe and illustrate PeakQC’s functionalities using different representative data sets, demonstrating its utility as a valuable tool for enhancing the quality and reliability of omics mass spectrometry analyses.

47 OTHER INSTRUMENTATION↗

Rapid quantitative analysis of trace elements in plutonium alloys using a handheld laser-induced breakdown spectroscopy (LIBS) device coupled with chemometrics and machine learning

Here, we present the first reported quantification of trace elements in plutonium via a portable laser-induced breakdown spectroscopy (LIBS) device and demonstrate the use of chemometric analysis to enhance the handheld device's sensitivity and precision. Quantification of trace elements such as iron and nickel in plutonium metal via LIBS is a challenging problem due to the complex nature of the plutonium optical emission spectra. While rapid analysis of plutonium alloys has been demonstrated using portable LIBS devices, such as the SciAps Z300, their detection limits for trace elements are severely constrained by their achievable pulse power and length, light collection optics, and detectors. In this paper, analytical methods are evaluated as a means to circumvent the detection constraints. Three chemometric methods often used in analytical spectroscopy are evaluated; principal component regression, partial least-squares regression, and artificial neural networks. These models are evaluated based on goodness-of-fit metrics, root mean-squared error, and their achievable limits of detection (LoDs). Partial least squares proved superior for determining content of iron and nickel in plutonium metal, yielding LoDs of 15 and 20 ppm, respectively. These results of identifying the undesirable trace elements in plutonium components are critical for applications such as fabricating radioisotope thermoelectric generators or nuclear fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A comparison of deep-learning-based inpainting techniques for experimental X-ray scattering

The implementation is proposed of image inpainting techniques for the reconstruction of gaps in experimental X-ray scattering data. The proposed methods use deep learning neural network architectures, such as convolutional autoencoders, tunable U-Nets, partial convolution neural networks and mixed-scale dense networks, to reconstruct the missing information in experimental scattering images. In particular, the recovered pixel intensities are evaluated against their corresponding ground-truth values using the mean absolute error and the correlation coefficient metrics. The results demonstrate that the proposed methods achieve better performance than traditional inpainting algorithms such as biharmonic functions. Overall, tunable U-Net and mixed-scale dense network architectures achieved the best reconstruction performance among all the tested algorithms, with correlation coefficient scores greater than 0.9980.

97 MATHEMATICS AND COMPUTING↗

Effective Missing Value Imputation Methods for Building Monitoring Data

To understand behaviors of natural and man-made events, such as energy consumption of buildings, which accounts for 40% of energy uses in the US, we deploy automated monitoring devices to record periodic observations. However, such experimental and observation data often contains problems and irregularities that have to be cleaned up before analyses. Due to various conditions affecting sensor operations, the communication channels, recording steps, or the recording media, the recorded data might have missing values, errors, or anomalous values. An effective way to clean up these problems is to replace these missing values, errors and anomalous values with expected values, a process generally known as imputation. In this work, we survey commonly used missing value imputation techniques and compare their performance on a set of building monitoring data. To compare the different types of sensor measurements with widely varying characteristics, we use normalized root mean squared error (NRMSE) as the key metric for the effectiveness of the imputation methods. We additionally consider periodicity and run time when considering comparing methods. Through extensive testing, we find that for small gap sizes, up to 8 consecutive missing values, linear interpolation performs the best; for larger gaps stretching up to 48 consecutive missing values, K-nearest neighbors provides the most accurate imputations; for even larger gaps, more computational intensive methods, such as matrix factorization, achieve the smallest NRMSE. Additionally, we observe that these computationally intensive algorithms not only provide accurate imputations for large gaps, but are also more robust across all types of sensors.

Cho, B↗

Visual Analytics of Performance of Quantum Computing Systems and Circuit Optimization

Driven by potential exponential speedups in business, security, and scientific scenarios, interest in quantum computing is surging. This interest feeds the development of quantum computing hardware, but several challenges arise in optimizing application performance for hardware metrics (e.g., qubit coherence and gate fidelity). In this work, we describe a visual analytics approach for analyzing the performance properties of quantum devices and quantum circuit optimization. Our approach allows users to explore spatial and temporal patterns in quantum device performance data and it computes similarities and variances in key performance metrics. Detailed analysis of the error properties characterizing individual qubits is also supported. We also describe a method for visualizing the optimization of quantum circuits. The resulting visualization tool allows researchers to design more efficient quantum algorithms and applications by increasing the interpretability of quantum computations.

Chae, Junghoon↗

Designing a parallel Feel-the-Way clustering algorithm on HPC systems

This paper introduces a new parallel clustering algorithm, named Feel-the-Way clustering algorithm, that provides better or equivalent convergence rate than the traditional clustering methods by optimizing the synchronization and communication costs. Our algorithm design centers on how to optimize three factors simultaneously: reduced synchronizations, improved convergence rate, and retained same or comparable optimization cost. To compare the optimization cost, we use the Sum of Square Error (SSE) cost as the metric, which is the sum of the square distance between each data point and its assigned clusters. Compared with the traditional MPI k-means algorithm, the new Feel-the-Way algorithm requires less communications among participating processes. As for the convergence rate, the new algorithm requires fewer number of iterations to converge. As for the optimization cost, it obtains the SSE costs that are close to the k-means algorithm. In the paper, we first design the full-step Feel-the-Way k-means clustering algorithm that can significantly reduce the number of iterations that are required by the original k-means clustering method. Next, we improve the performance of the full-step algorithm by adopting an optimized sampling-based approach, named reassignment-history-aware sampling. Our experimental results show that the optimized sampling-based Feel-the-Way method is significantly faster than the widely used k-means clustering method, and can provide comparable optimization costs. More extensive experiments with several synthetic datasets and real-world datasets (e.g., MNIST, CIFAR-10, ENRON, and PLACES-2) show that the new parallel algorithm can outperform the open source MPI k-means library by up to 110% on a high-performance computing system using 4,096 CPU cores. In addition, the new algorithm can take up to 51% fewer iterations to converge than the k-means clustering algorithm.

97 MATHEMATICS AND COMPUTING↗

Validation of the High-Resolution Salish Sea Tidal Hydrodynamic Model

In this study, a tidal hydrodynamic model was developed and validated to simulate tidal currents in Puget Sound, Washington, to support tidal energy resource characterization using the unstructured-grid, Finite Volume Community Ocean Model (FVCOM). The Salish Sea tidal hydrodynamic model was driven by tides along two open boundaries at the entrance of the Strait of Juan de Fuca and north end of Georgia Strait, and river flows from 19 major rivers in the Salish Sea. To simulate the tidal current in Puget Sound, a high-resolution model grid is required to accurately represent the complex coastlines and bathymetry. The spatial resolution of the model grid varies from ~10 m near river boundaries and ~30 m in small tidal channels and estuaries to near 1000 m inside Georgia Strait and at the open boundaries. Model validation was carried out by comparing simulated and observed water levels at 12 tidal stations and currents at 135 Acoustic Doppler Current Profiler stations in the model domain. A set of model performance metrics, including root mean square error, scatter index, bias, and linear correlation coefficient, were used to quantify the model skills in simulating the tidal hydrodynamics in Puget Sound. Error statistics showed an overall good agreement between simulated and observed tidal elevations and currents, which demonstrated that the Puget Sound tidal model can be used to accurately characterize the tidal stream energy resource in Puget Sound.

16 TIDAL AND WAVE POWER↗

Enter Gaussian Mixture Modeling Extensions for Improved False Discovery Rate Estimation in GC-MS Metabolomics

Identifying small molecules (e.g., metabolites) is key towards driving scientific advancement in metabolomics, and gas chromatography–mass spectrometry (GC-MS) is an analytic method that may be applied to facilitate this process. The typical GC-MS identification workflow involves quantifying the similarity of an observed sample spectrum and other features (e.g. retention index) to that of several references, noting the compound of the best-matching reference spectrum as the identified metabolite. While a deluge of similarity metrics exists, none characterize the error rate of generated identifications, thereby presenting an unknown risk of false identification or discovery. To quantify this unknown risk, we propose a model-based framework for estimating the false discovery rate (FDR) among a set of identifications. Extending the traditional mixture modeling framework, our method incorporates both similarity score and experimental information in estimating the FDR. We apply these models to identification lists derived from across 548 samples of varying complexity and sample type (e.g., fungal species, standard mixtures, etc.), comparing their performance to that of the traditional Gaussian mixture model (GMM). Through simulation, we additionally assess the impact of reference library size on the accuracy of FDR estimates. In comparing the best performing model extensions to the GMM, our results indicate relative decreases in median absolute estimation error (MAE) ranging from 12% to 70%, based on comparisons of the median MAEs across all hit-lists. Results indicate that these relative performance improvements generally hold despite library size, however FDR estimation error typically worsens as the set of reference compounds diminishes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Semi-supervised Hybrid Machine Learning Framework for the Qualification of Resistance Spot Welds

• Industries requiring high structural integrity, including automotive, aerospace, and construction, place considerable significance on weld quality classification. • The inspection normally involves human expertise through predefined quality metrics that are subjective, error-prone, and time-intensive • The challenge to classification model development is the scarcity of labeled data and imbalanced distributions in the data that are labeled. • This work develops a new hybrid methodology that achieves clustering using KMeans++ together with supervised classification to overcome these challenges. • The ensemble-based classifiers were identified as optimal, with accuracy enhancements of up to 8% using the pseudo-labeled dataset. • The work provides practical insight into feature engineering and machine learning integration in industrial quality assurance applications.

Rogers, Jeremy K. [Savannah River National Laborat↗

Machine Learning Analysis of Temperature-Strain Relationships for Structural Health Monitoring of Pipes: Self-powered wireless sensor system for health monitoring of liquid-sodium cooled fast reactors

This report presents machine learning (ML) analysis of temperature-strain relationships for structural health monitoring of nuclear reactor stainless steel (SS) pipes with the strain gauge sensor directly printed on the pipe with a 3D conformal aerosol jet printer. We investigate correlations for two sensor pairs installed on the same SS304 pipe: commercial K-type thermocouple with a printed gold strain gauge (TC3-SG3), and commercial K-type thermocouple with commercial Kyowa strain gauge (TC0-SG0). The temperature ranges for the sensor pairs TC0-SG0 and TC3-SG3 are 20.00°C to 266.37°C and 39.95°C to 219.28°C respectively. ML algorithms in this study include Linear Regression (baseline method), Ridge Regression, Lasso Regression, and Gradient Boosting. Performance evaluation metrics include Root Mean Square Error (RMSE), Mean Square Error (MSE), Mean Absolute Error (MAE), R 2 Score, and Explained Variance. Using advanced feature engineering techniques, we extracted 27 temperature-based features and 30 strategic inclusion features. The best performance was obtained with the Gradient Boosting method, which achieves prediction accuracy of R 2 = 0.9999 and RMSE = 7.69 μStrain for TC0-SG0, and R 2 = 0.9998 and RMSE = 18.03 μStrain for TC3-SG3. While the temperature-strain correlations are weaker for the gauge directly printed on the pipe than for the commercial strain gauge, deployment-ready performance exceeding industry standards is achieved for both sensor pairs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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↗