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DOE OSTI2022

Calculating the grain boundary inclination of voxelated grain structures using a smoothing algorithm

We have developed a flexible method for calculating the grain boundary (GB) inclinations of voxelated grain structure data using smoothing algorithms. We compared the performance of four algorithms: the linear interpolation, Allen–Cahn, level-set, and vertex algorithms. We assessed their accuracy using 2D and 3D cases with known inclinations. The vertex algorithm provided the best balance between accuracy and efficiency for 2D structures while the linear interpolation algorithm provided the best balance for 3D structures. We compared the GB inclinations calculated using our smoothing method on a 3D high energy X-ray diffraction microscopy (HEDM) dataset to those determined by meshing the GBs. The two approaches determined similar GB plane distributions, though they varied significantly at triple junctions. In conclusion, the smoothing method was demonstrated for two sources of 3D voxelated grain structures: HEDM data and results from Monte Carlo Potts grain growth simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Quantifying and Visualizing Uncertainty for Source Localisation in Electrocardiographic Imaging

Electrocardiographic imaging (ECGI) presents a clinical opportunity to noninvasively understand the sources of arrhythmias for individual patients. To help increase the effectiveness of ECGI, we provide new ways to visualise associated measurement and modelling errors. Here, we study source localisation uncertainty in two steps: First, we perform Monte Carlo simulations of a simple inverse ECGI source localisation model with error sampling to understand the variations in ECGI solutions. Second, we present multiple visualisation techniques, including confidence maps, level-sets, and topology-based visualisations, to better understand uncertainty in source localization. Our approach offers a new way to study uncertainty in the ECGI pipeline.

47 OTHER INSTRUMENTATION↗

DOE OSTI2019

Relaxation algorithms for matrix completion, with applications to seismic travel-time data interpolation

Travel time tomography is used to infer the underlying three-dimensional wavespeed structure of the Earth by fitting seismic travel time data collected at surface stations. Data interpolation and denoising techniques are important pre-processing steps that use prior knowledge about the data, including parsimony in the frequency and wavelet domains, low-rank structure of matricizations, and local smoothness. In this work, we show how local smoothness structure can be combined with low rank constraints using level-set optimization formulations, and develop a new relaxation algorithm that can efficiently solve these joint problems. In the seismology setting, we use the approach to interpolate missing stations and de-noise observed stations. The new approach is competitive with alternative algorithms, and offers new functionality to interpolate observed data using both smoothness and low rank structure in the presence of data fitting constraints.

constrained optimization↗

DOE OSTI2024

Ensemble Kalman inversion of induced polarization data

SUMMARY This paper explores the applicability of ensemble Kalman inversion (EKI) with level-set parametrization for solving geophysical inverse problems. In particular, we focus on its extension to induced polarization (IP) data with uncertainty quantification. IP data may provide rich information on characteristics of geological materials due to its sensitivity to characteristics of the pore–grain interface. In many IP studies, different geological units are juxtaposed and the goal is to delineate these units and obtain estimates of unit properties with uncertainty bounds. Conventional inversion of IP data does not resolve well sharp interfaces and tends to reduce and smooth resistivity variations, while not readily providing uncertainty estimates. Recently, it has been shown for DC resistivity that EKI is an efficient solver for inverse problems which provides uncertainty quantification, and its combination with level set parametrization can delineate arbitrary interfaces well. In this contribution, we demonstrate the extension of EKI to IP data using a sequential approach, where the mean field obtained from DC resistivity inversion is used as input for a separate phase angle inversion. We illustrate our workflow using a series of synthetic and field examples. Variations with uncertainty bounds in both DC resistivity and phase angles are recovered by EKI, which provides useful information for hydrogeological site characterization. Although phase angles are less well-resolved than DC resistivity, partly due to their smaller range and higher percentage data errors, it complements DC resistivity for site characterization. Overall, EKI with level set parametrization provides a practical approach forward for efficient hydrogeophysical imaging under uncertainty.

Geochemistry & Geophysics↗

DOE OSTI2022

Fiber Uncertainty Visualization for Bivariate Data With Parametric and Nonparametric Noise Models

Visualization and analysis of multivariate data and their uncertainty are top research challenges in data visualization. Constructing fiber surfaces is a popular technique for multivariate data visualization that generalizes the idea of level-set visualization for univariate data to multivariate data. Here, in this paper, we present a statistical framework to quantify positional probabilities of fibers extracted from uncertain bivariate fields. Specifically, we extend the state-of-the-art Gaussian models of uncertainty for bivariate data to other parametric distributions (e.g., uniform and Epanechnikov) and more general nonparametric probability distributions (e.g., histograms and kernel density estimation) and derive corresponding spatial probabilities of fibers. In our proposed framework, we leverage Green's theorem for closed-form computation of fiber probabilities when bivariate data are assumed to have independent parametric and nonparametric noise. Additionally, we present a nonparametric approach combined with numerical integration to study the positional probability of fibers when bivariate data are assumed to have correlated noise. For uncertainty analysis, we visualize the derived probability volumes for fibers via volume rendering and extracting level sets based on probability thresholds. We present the utility of our proposed techniques via experiments on synthetic and simulation datasets.

97 MATHEMATICS AND COMPUTING↗

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

Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles

Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of en-semble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introduces a deep-learning-based approach to learning the level-set uncertainty for two-dimensional ensemble data with a multivariate Gaussian noise assumption. We train the model using the first few time steps from time-varying ensemble data in our workflow. We demonstrate that our trained model accurately infers uncertainty in level sets for new time steps and is up to 170X faster than that of the original probabilistic model with serial computation and 10X faster than that of the original parallel computation.

Han, Mengjiao↗

DOE OSTI2022

BDEM (Discrete-element-simulator for high-solids granular flows) [SWR-22-72]

BDEM is a discrete element method based simulation tool developed specifically for modeling high-solids granular flows that include polydispersity, heat-transfer, moving boundaries and chemistry. Our solver provides facilities for simulating spherical/non-spherical particles with modified contact and friction models in complex dynamic geometries defined using level-sets or triangulated files. The solver is developed on top of NREL's open-source performance portable library, AMReX, providing parallel execution capabilities on current and upcoming high-performance-computing (HPC) architectures. Simulations at the scale of several millions to billion particles have been performed using this software on large scale computing resources. This software can be applied to non-reacting solids dominant flows in silos, hoppers and screw conveyors as well as in high temperature reacting systems such as screw kilns and auger reactors.

Sitaraman, Hariswaran↗

DOE OSTI2021

idaholab/malamute

MALAMUTE combines MOOSE module functionality with realistic materials and geometries for arbitrary-Eulerian-Lagrangian (ALE) and level-set based laser melting and welding applications and electric-field assisted sintering (EFAS) applications.

Icenhour, Casey [Idaho National Lab. (INL), Idaho ↗

DOE OSTI2021

Moose Application Library For Advanced Manufacturing Utilities

Lindsay, AlexanderD.↗

DOE OSTI2021

EGR Dilution and Fuel Property Effects on High-Efficiency Spark-Ignition Flames

Modern spark ignition internal combustion engines rely on fast combustion rates and high dilution to achieve high brake thermal efficiencies. To accomplish this, new engine designs have moved towards increased tumble ratios and stroke-to-bore ratios. Increased tumble ratios correlate positively with increases in turbulent kinetic energy and improved fuel and residual gas mixing, all of which favor faster and more efficient combustion. Longer stroke-to-bore ratios allow higher geometric compression ratios and use of late intake valve closing to control peak compression pressures and temperatures. The addition of dilution to improve efficiency is limited by the resulting increase in combustion instabilities manifested by cycle-to-cycle variability. A number of effects - preferential diffusion, turbulence-combustion interactions, stochastic flow patterns, laminar-turbulent flame kernel transitions, and relative length and velocity scales between flame and turbulence - are believed to be responsible for the increase in cycle-to-cycle variations, where their contributions are likely interlinked. Several studies have shown the influence of stochastic flow characteristics on the nature of combustion instabilities, such as velocity patterns on flame kernel formation and cycle-to-cycle variations in residual gas. However, few have focused on the specific effects of fuel properties. The objective of this work is to contrast the effects of dilution on propane stoichiometric combustion against gasoline. Dilution tolerance experiments were conducted in a purpose-built high stroke-to-bore ratio single cylinder engine with both gasoline and LPG. Three-dimensional full cycle computational fluid dynamics (CFD) simulations employing a level-set combustion approach and Reynolds averaged Navier-Stokes (RANS) turbulence modeling was used to qualitatively assess the changes in length and velocity scales for turbulence and the flame. The experimental results showed that LPG can tolerate higher exhaust gas recirculation (EGR) dilution under a variety of conditions. Analysis of CFD simulations showed that propane flames are likely less sensitive to influences from the flow field due to less thickening of the flame and higher effective flame speeds.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1993

Reconfigurable fuzzy cell

This invention relates to a reconfigurable fuzzy cell comprising a digital control programmable gain operation amplifier, an analog-to-digital converter, an electrically erasable PROM, and 8-bit counter and comparator, and supporting logic configured to achieve in real-time fuzzy systems high throughput, grade-of-membership or membership-value conversion of multi-input sensor data. The invention provides a flexible multiplexing-capable configuration, implemented entirely in hardware, for effectuating S-, Z-, and PI-membership functions or combinations thereof, based upon fuzzy logic level-set theory. A membership value table storing 'knowledge data' for each of S-, Z-, and PI-functions is contained within a nonvolatile memory for storing bits of membership and parametric information in a plurality of address spaces. Based upon parametric and control signals, analog sensor data is digitized and converted into grade-of-membership data. In situ learn and recognition modes of operation are also provided.

Salazar, George A.↗

NASA NTRS1996

Dynamical Modeling of Surface Tension

In a recent review it is said that free-surface flows 'represent some of the difficult remaining challenges in computational fluid dynamics'. There has been progress with the development of new approaches to treating interfaces, such as the level-set method and the improvement of older methods such as the VOF method. A common theme of many of the new developments has been the regularization of discontinuities at the interface. One example of this approach is the continuum surface force (CSF) formulation for surface tension, which replaces the surface stress given by Laplace's equation by an equivalent volume force. Here, we describe how CSF formulation might be made more useful. Specifically, we consider a derivation of the CSF equations from a minimization of surface energy as outlined by Jacqmin (1996). This reformulation suggests that if one eliminates the computation of curvature in terms of a unit normal vector, parasitic currents may be eliminated. For this reformulation to work, it is necessary that transition region thickness be controlled. Various means for this, in addition to the one discussed by Jacqmin (1996), are discussed.

Brackbill, Jeremiah U.↗

NASA NTRS2019

Image Processing Methods for Coronal Hole Segmentation, Matching, and Map Classification

The paper presents the results from a multi-year effort to develop and validate image processing methods forselecting the best physical models based on solar image observations. The approach consists of selecting the physical models based on their agreement with coronal holes extracted from the images. Ultimately, the goal is to use physical models to predict geomagnetic storms. We decompose the problem into three subproblems: (i) coronal hole segmentation based on physical constraints, (ii) matching clusters of coronal holes between different maps, and (iii) physical map classification. For segmenting coronal holes, we develop a multi-modal method that uses segmentation maps from three different methods to initialize a level-set method that evolves the initial coronal hole segmentation to the magnetic boundary. Then, we introducea new method based on Linear Programming for matchingclusters of coronal holes. The final matching is then performedusing Random Forests. The methods were carefully validatedusing consensus maps derived from multiple readers, manualclustering, manual map classification, and method validation for50 maps. The proposed multi-modal segmentation method significantly outperformed SegNet, U-net, Henney-Harvey, and FCNby providing accurate boundary detection. Overall, the methodgave a 95.5% map classification accuracy.

Jatla, Venkatesh↗

DOE OSTI2019

Learning nonlinear level sets for dimensionality reduction in function approximation

We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime. Specifically, we exploit reversible networks (RevNets) to learn nonlinear level sets of a high-dimensional function and parameterize its level sets in low-dimensional spaces. A new loss function was designed to utilize samples of the target functions' gradient to encourage the transformed function to be sensitive to only a few transformed coordinates. The NLL approach is demonstrated by applying it to three 2D functions and two 20D functions for showing the improved approximation accuracy with the use of nonlinear transformation, as well as to an 8D composite material design problem for optimizing the buckling-resistance performance of composite shells of rocket inter-stages.

Zhang, Guannan↗

DOE OSTI2023

A Level Set Model for Structured Mesh Representation of Fibrous Preforms used in Composites Manufacturing

Here, a model for implicit representation of fibrous and woven preforms used for composites manufacturing is described. The method is based on a level set function defined on a structured mesh to implicitly capture the complex fiber and weave geometries. Since most software packages used to model woven preforms are based on unstructured mesh, a numerical model for transforming a discretized surface to a structured mesh representation and vice-a-versa is presented. Specific emphasis is on scalable computation of a level set function for large and complex 3D woven structures from a triangulated surface of the smallest unit (yarn). The model is applied to capture a periodic 3D layered 5-harness satin (5HS) weave geometry on a structured mesh. Geometric transformations needed to efficiently compute the level set function for the 3D structure on a high resolution mesh are described. Effects of mesh resolution on the geometric features such as number of resolved fibers, effective fiber size, and the surface area to volume ratio of the iso-surface are analyzed. Using the distance property of the level set function, an approach to evaluate the structure function resulting from transient evolving topology representing densification due to matrix phase depositions is also presented. The approach captures transition of the geometric characteristic from fiber governed at early stages of densification to yarn governed at the terminal stage.

36 MATERIALS SCIENCE↗

DOE OSTI2022

High-fidelity pool boiling simulations on multiple nucleation sites using interface capturing method

Boiling has proved to be one of the most efficient means for heat transfer and is a very important phenomenon during severe accident scenarios in light water reactors. High-fidelity pool boiling simulations can provide a numerical database for improving mechanistic boiling models by allowing for specific evaluation of interactions among bubbles. Previously published pool boiling simulations investigated two nucleation sites in which bubble growth at one site suppressed nucleation at the other site. Based on previous study results, more complicated interface-capturing simulations on pool boiling were conducted using PHASTA code with locally refined unstructured mesh. First, different boundary conditions (BCs) were assessed to support robustness and reproducibility of the boiling model. Then, a scale study was conducted at a larger domain with nine nucleation sites where either nine or four nucleation sites are activated. Involving more nucleation sites increased the complexity of bubble interactions from surrounding sites. Finally, bubble departure behavior influenced by wall heat flux was investigated. In this work, when heat flux was increased, the order of bubble departure changed, but diagonal bubbles always departed after one another. The departure time interval between the first and second bubble reduced as heat flux increased. The corresponding frequency was almost linearly proportional to the heat flux. In addition, bubble departure behavior was found to be greatly influenced by the nucleation site pattern. Multiple nucleation sites resulted in superimposed inhibitive effects from surrounding sites to each bubble, which extensively delayed the departure. This new observation was not discussed in previously published works. The work presented here provides new insight on the fundamental understanding of boiling phenomena, contributes to the development of a 3D multiphase computational fluid dynamics (M-CFD) model, and provides a more comprehensive database for data-driven pool boiling studies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗