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DOE OSTI2017

An improved random walk algorithm for the implicit Monte Carlo method

In this work, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequency-dependent opacities. To date, the RW method has only been implemented in “fully-gray” form; that is, the multigroup IMC opacities are group-collapsed over the full frequency domain of the problem to obtain a gray diffusion problem for RW. This formulation works well for problems with large spatial cells and/or opacities that are weakly dependent on frequency; however, the efficiency of the RW method degrades when the spatial cells are thin or the opacities are a strong function of frequency. To address this inefficiency, we introduce a RW frequency group cutoff in each spatial cell, which divides the frequency domain into optically thick and optically thin components. In the modified algorithm, opacities for the RW diffusion problem are obtained by group-collapsing IMC opacities below the frequency group cutoff. Particles with frequencies above the cutoff are transported via standard IMC, while particles below the cutoff are eligible for RW. This greatly increases the total number of RW steps taken per IMC time-step, which in turn improves the efficiency of the simulation. We refer to this new method as Partially-Gray Random Walk (PGRW). We present numerical results for several multigroup radiative transfer problems, which show that the PGRW method is significantly more efficient than standard RW for several problems of interest. In general, PGRW decreases runtimes by a factor of ∼2–4 compared to standard RW, and a factor of ∼3–6 compared to standard IMC. While PGRW is slower than frequency-dependent Discrete Diffusion Monte Carlo (DDMC), it is also easier to adapt to unstructured meshes and can be used in spatial cells where DDMC is not applicable. This suggests that it may be optimal to employ both DDMC and PGRW in a single simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Capabilities of multivariate Bayesian inference toward seismic hazard assessment

Multivariate Bayesian analysis can bring significant benefits to seismic hazard analysis: Its multivariate feature enables computing scalar and vector hazard without making any approximations; Correlations between intensity measures are implicitly modeled, permitting direct simulation of ground motion selection tools such as the conditional mean spectrum and the generalized conditioning intensity measure; and Its updating feature enables a seamless integration of new ground motion data into the hazard results. Here, we first develop a multivariate Bayesian ground motion model through the NGA-West2 database. The model functional form considers fault-type, magnitude, and distance dependencies, and also the linear and the rock intensity dependent site response. We use a hybrid Markov Chain Monte Carlo sampling to perform Bayesian inference consisting of Gibbs step and a multilevel Metropolis-Hastings step. We then perform several checks on the model and note that its performance is satisfactory. Finally, we illustrate the merits of this multivariate Bayesian analysis, which include: ground motion model updating with ground motion data recorded in the last four years not part of the NGA-West2 database; computation of scalar and vector seismic hazard using the un-updated and updated ground motion models for Los Angeles, CA; and simulation of the conditional mean spectrum under scalar and vector IM conditioning while accounting for different sources of aleatoric and epistemic uncertainties.

58 GEOSCIENCES↗

DOE OSTI2018

High resolution viscous fingering simulation in miscible displacement using a p-adaptive discontinuous Galerkin method with algebraic multigrid preconditioner

High resolution simulation of viscous fingering can offer an accurate and detailed prediction for subsurface engineering processes involving fingering phenomena. The fully implicit discontinuous Galerkin (DG) method has been shown to be an accurate and stable method to model viscous fingering with high Peclet number and mobility ratio. In this study, we present two techniques to speedup large scale simulations of this kind. The first technique relies on a simple p-adaptive scheme in which high order basis functions are employed only in elements near the finger fronts where the concentration has a sharp change. As a result, the number of degrees of freedom is significantly reduced and the simulation yields almost identical results to the more expensive simulation with uniform high order elements throughout the mesh. The second technique for speedup involves improving the solver efficiency. We present an algebraic multigrid (AMG) preconditioner which allows the DG matrix to leverage the robust AMG preconditioner designed for the continuous Galerkin (CG) finite element method. The resulting preconditioner works effectively for fixed order DG as well as p-adaptive DG problems. Finally, with the improvements provided by the p-adaptivity and AMG preconditioning, we can perform high resolution three-dimensional viscous fingering simulations required for miscible displacement with high Peclet number and mobility ratio in greater detail than before for well injection problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Synergic Effects of Surface Chemistry and Applied Potentials on the Kinetics of the Electrocatalytic Oxygen Evolution Reaction in IrO 2

Improving the efficacy of the oxygen evolution reaction (OER) through water oxidation is critical for advancing photoelectrochemical water splitting. Among the catalysts, IrO 2 exhibits a high OER catalytic activity and stability under acidic conditions. The OER mechanism in this system has been a topic of intense research; however, many mechanistic understandings are lacking. In this work, we carried out first-principles calculations with an implicit solvation model at a constant potential to study the OER behavior on the IrO 2 (110) surface. We find that the surface hydrogen coverage has a significant effect on OER kinetics and transition states. We then develop a microkinetics model that accounts for the continuous evolution of both OER activation energy and hydrogen coverage as a function of an applied potential. We show that this inclusion leads to significant improvement in the simulated Tafel plot compared to available experiments. In conclusion, our results point to a complex interplay between surface chemistry and the applied potential on OER kinetics.

08 HYDROGEN↗

NASA NTRS1998

Effect of Apex Flap Deflection on Vertical Tail Buffeting

A computational study of the effect of vortex breakdown location on vertical tail buffeting is conducted. The position of the breakdown is modified by employing an apex flap deflected by an experimentally determined optimal angle. The delayed breakdown flow and buffeting response is then compared to the nominal undeflected case. This multidisciplinary problem is solved sequentially for the fluid flow, the elastic tail deformations and the grid displacements. The fluid flow is simulated by time accurately solving the unsteady, compressible, Reynolds-averaged Navier-Stokes equations using an implicit, upwind, flux-difference splitting finite volume scheme. The elastic vibrations of the tails are modeled by uncoupled bending and torsion beam equations. These equations are solved accurately in time using the Galerkin method and a five-stage Runge-Kutta-Verner scheme. The grid for the fluid dynamics calculations is continuously deformed using interpolation functions to disperse the displacements smoothly throughout the computational domain. An angle-of-attack of 35 deg.is chosen such that the wing primary-vortex cores experience vortex breakdown and the resulting turbulent wake flow impinges on tile vertical tails. The dimensions and material properties of the vertical tails are chosen such that the deflections are large enough to insure interaction with the flow, and the natural frequencies are high enough to facilitate a practical computational solution. Results are presented for a baseline uncontrolled buffeting case and a delayed breakdown case in which the apex flap has been deflected 15 deg. The flap was found to be very effective in delaying the breakdown, increasing the location from 50%c to 94%c, which resulted in a 6% increase in lift coefficient and pitching moment. However, the integrated buffet loads and tip responses were roughly equivalent for the two cases.

Massey, Steven J.↗

DOE OSTI2022

Crystal plasticity modeling of strain-induced martensitic transformations to predict strain rate and temperature sensitive behavior of 304 L steels: Applications to tension, compression, torsion, and impact

This paper advances crystallographically-based Olson-Cohen (direct γ → α’) and deformation mechanism (indirect γ→ε→α’) phase transformation models for predicting strain-induced austenite to martensite transformation. Here, the advanced transformation models enable predictions of not only strain-path sensitive, but also of strain-rate and temperature sensitive deformation of polycrystalline stainless steels (SSs). The deformation of constituent grains in SSs is modeled as a combination of anisotropic elasticity, crystallographic slip, and phase transformation, while the hardening is based on the evolution of dislocation density and explicit shifts in phase fractions. Such grain-scale deformation is implemented within the meso-scale elasto-plastic self-consistent (EPSC) homogenization model, which is coupled with the implicit finite element (FE) method to provide a constitutive response at each FE integration point for solving boundary value problems at the macro-scale. Parameters pertaining to the hardening and transformation models within FEEPSC are calibrated and validated on a suite of data including flow curves and phase fractions for monotonic compression, tension, and torsion as a function of strain-rate and temperature for wrought and additively manufactured (AM) SS304L. To illustrate the potential and accuracy of the integrated multi-level FE-EPSC simulation framework, geometry, mechanical response, phase fractions, and texture evolution are simulated during gas-gun impact deformation of a cylinder and quasi-static tension of a notched specimen made of AM SS304L. Details of the simulation framework, comparison between experimental and simulation results, and insights from the results are presented and discussed.

304L steels↗

DOE OSTI2014

An environment-dependent semi-empirical tight binding model suitable for electron transport in bulk metals, metal alloys, metallic interfaces, and metallic nanostructures. I. Model and validation

Semi-empirical Tight Binding (TB) is known to be a scalable and accurate atomistic representation for electron transport for realistically extended nano-scaled semiconductor devices that might contain millions of atoms. In this paper, an environment-aware and transferable TB model suitable for electronic structure and transport simulations in technologically relevant metals, metallic alloys, metal nanostructures, and metallic interface systems are described. Part I of this paper describes the development and validation of the new TB model. The new model incorporates intra-atomic diagonal and off-diagonal elements for implicit self-consistency and greater transferability across bonding environments. The dependence of the on-site energies on strain has been obtained by appealing to the Moments Theorem that links closed electron paths in the system to energy moments of angular momentum resolved local density of states obtained ab initio. The model matches self-consistent density functional theory electronic structure results for bulk face centered cubic metals with and without strain, metallic alloys, metallic interfaces, and metallic nanostructures with high accuracy and can be used in predictive electronic structure and transport problems in metallic systems at realistically extended length scales.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1992

Algebraic surface design and finite element meshes

Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.

Bajaj, Chandrajit L.↗

DOE OSTI2019

Pair and many-body interactions between ligated Au nanoparticles

Here, we report the results of molecular dynamics simulations of the properties of a pseudo-atom (united atom) model of dodecane thiol ligated 5-nm diameter gold nanoparticles (AuNPs) in a vacuum as a function of ligand coverage and particle separation in three states of aggregation, namely, the isolated AuNPs, the isolated pair of AuNPs, and a square lattice of four AuNPs. Our calculations show that the ligand density along a radius emanating from the core of an isolated AuNP has the same gross features for all values of the coverage; it oscillates around a constant value up to a distance along the chain corresponding to the position of the fourth pseudo-atom and then smoothly decays to zero, reflecting both the restricted conformations of the chain near the core surface and the larger numbers of conformations available further from the core. Interaction between two AuNPs generates changes in the ligand distributions of each. We examine the structure and general shape of the ligand envelope as a function of the coverage and demonstrate that the equilibrium structure of the envelope and the deformation of that envelope generated by interaction between the NPs are coverage-dependent so that the shape, depth, and position of the minimum of the potential of mean force display a systematic dependence on the ligand coverage. We propose an accurate analytical description of the calculated potential of mean force as a function of a set of parameters that scale linearly with the ligand coverage. Noting that the conformational freedom of the ligands implies that multiparticle induced deviations from additivity of the pair potential of mean force are likely important; we define and calculate a “bond stretching” effective pair potential of mean force for a square lattice of particles that contains, implicitly, both the three- and four-NP contributions. We find that the bond stretching effective pair potential of mean force in this cluster has a different minimum and a different well depth from the isolated pair potential of mean force. Previous work has found that the three-particle contribution to deviation from pair additivity is monotonically repulsive, whereas we find that the combined three- and four-particle contributions have an attractive well, implying that the three- and four-particle contributions are of comparable magnitude but opposite sign, thereby suggesting that even higher order correction terms likely play a significant role in the behavior of dense assemblies of many nanoparticles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Verification of an energy-conserving semi-implicit electrostatic particle-in-cell scheme for modeling high-density plasma at scale

A verification study of a semi-implicit energy-conserving electrostatic particle-in-cell algorithm is presented. The algorithm relaxes the time-step and mesh-size constraints that require resolution of the plasma period and Debye length associated with traditional explicit momentum-conserving particle-in-cell algorithms. Physical implications and applicability of using the semi-implicit scheme for modeling high-density plasmas are discussed. Where possible, numerical results are compared against analytical solutions. The simulation results indicate that the algorithm is stable at time steps larger than twice the inverse plasma frequency and cell sizes larger than the Debye length. It is found that the algorithm gives adequate results, provided that the distribution function and the spatiotemporal scales dictating the physics of the problem are resolved. As such, the algorithm may provide a robust method for kinetic modeling of high-density plasmas at scale.

Cyclotron resonance↗

DOE OSTI2025

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction

4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. Here, we use a forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued 4D object coordinates. Unlike previous neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Managing genomic variant calling workflows with Swift/T

Bioinformatics research is frequently performed using complex workflows with multiple steps, fans, merges, and conditionals. This complexity makes management of the workflow difficult on a computer cluster, especially when running in parallel on large batches of data: hundreds or thousands of samples at a time. Scientific workflow management systems could help with that. Many are now being proposed, but is there yet the “best” workflow management system for bioinformatics? Such a system would need to satisfy numerous, sometimes conflicting requirements: from ease of use, to seamless deployment at peta- and exa-scale, and portability to the cloud. We evaluated Swift/T as a candidate for such role by implementing a primary genomic variant calling workflow in the Swift/T language, focusing on workflow management, performance and scalability issues that arise from production-grade big data genomic analyses. In the process we introduced novel features into the language, which are now part of its open repository. Additionally, we formalized a set of design criteria for quality, robust, maintainable workflows that must function at-scale in a production setting, such as a large genomic sequencing facility or a major hospital system. The use of Swift/T conveys two key advantages. (1) It operates transparently in multiple cluster scheduling environments (PBS Torque, SLURM, Cray aprun environment, etc.), thus a single workflow is trivially portable across numerous clusters. (2) The leaf functions of Swift/T permit developers to easily swap executables in and out of the workflow, which makes it easy to maintain and to request resources optimal for each stage of the pipeline. While Swift/T’s data-level parallelism eliminates the need to code parallel analysis of multiple samples, it does make debugging more difficult, as is common for implicitly parallel code. Nonetheless, the language gives users a powerful and portable way to scale up analyses in many computing architectures.

Science & Technology - Other Topics↗

NASA NTRS1984

The spatial structure of terrain - A process signal in satellite digital images

Pattern recognition procedures applied to Landsat imagery carry an implicit assumption that the digital data are independently distributed. That assumption is incorrect over virtually any terrain. Deviations from independence occur because slopes follow a systematic pattern of variation arising from the slope-forming processes. That pattern can be identified using the stochastic process methodology of Box and Jenkins.Angles of adjacent slopes are autocorrelated and the bidirectional reflectance function transfers these systematic slope changes to the sensor. Imagery becomes autocorrelated through this transfer. Autocorrelation in the imagery can be removed through direct calculation from a digital elevation model or by use of stochastic process methodology. The latter has the advantage that the residuals are white noise; and it is applicable in any area, even where a D.E.M. is unavailable. The stochastic process signal can be used to study terrain processes.

Craig, R. G.↗

DOE OSTI2016

Anatomical pulmonary magnetic resonance imaging segmentation for regional structure-function measurements of asthma

Purpose: Pulmonary magnetic-resonance-imaging (MRI) and x-ray computed-tomography have provided strong evidence of spatially and temporally persistent lung structure-function abnormalities in asthmatics. This has generated a shift in their understanding of lung disease and supports the use of imaging biomarkers as intermediate endpoints of asthma severity and control. In particular, pulmonary {sup 1}H MRI can be used to provide quantitative lung structure-function measurements longitudinally and in response to treatment. However, to translate such biomarkers of asthma, robust methods are required to segment the lung from pulmonary {sup 1}H MRI. Therefore, their objective was to develop a pulmonary {sup 1}H MRI segmentation algorithm to provide regional measurements with the precision and speed required to support clinical studies. Methods: The authors developed a method to segment the left and right lung from {sup 1}H MRI acquired in 20 asthmatics including five well-controlled and 15 severe poorly controlled participants who provided written informed consent to a study protocol approved by Health Canada. Same-day spirometry and plethysmography measurements of lung function and volume were acquired as well as {sup 1}H MRI using a whole-body radiofrequency coil and fast spoiled gradient-recalled echo sequence at a fixed lung volume (functional residual capacity + 1 l). We incorporated the left-to-right lung volume proportion prior based on the Potts model and derived a volume-proportion preserved Potts model, which was approximated through convex relaxation and further represented by a dual volume-proportion preserved max-flow model. The max-flow model led to a linear problem with convex and linear equality constraints that implicitly encoded the proportion prior. To implement the algorithm, {sup 1}H MRI was resampled into ∼3 × 3 × 3 mm{sup 3} isotropic voxel space. Two observers placed seeds on each lung and on the background of 20 pulmonary {sup 1}H MR images in a randomized dataset, on five occasions, five consecutive days in a row. Segmentation accuracy was evaluated using the Dice-similarity-coefficient (DSC) of the segmented thoracic cavity with comparison to five-rounds of manual segmentation by an expert observer. The authors also evaluated the root-mean-squared-error (RMSE) of the Euclidean distance between lung surfaces, the absolute, and percent volume error. Reproducibility was measured using the coefficient of variation (CoV) and intraclass correlation coefficient (ICC) for two observers who repeated segmentation measurements five-times. Results: For five well-controlled asthmatics, forced expiratory volume in 1 s (FEV{sub 1})/forced vital capacity (FVC) was 83% ± 7% and FEV{sub 1} was 86 ± 9%{sub pred}. For 15 severe, poorly controlled asthmatics, FEV{sub 1}/FV C = 66% ± 17% and FEV{sub 1} = 72 ± 27%{sub pred}. The DSC for algorithm and manual segmentation was 91% ± 3%, 92% ± 2% and 91% ± 2% for the left, right, and whole lung, respectively. RMSE was 4.0 ± 1.0 mm for each of the left, right, and whole lung. The absolute (percent) volume errors were 0.1 l (∼6%) for each of right and left lung and ∼0.2 l (∼6%) for whole lung. Intra- and inter-CoV (ICC) were <0.5% (>0.91%) for DSC and <4.5% (>0.93%) for RMSE. While segmentation required 10 s including ∼6 s for user interaction, the smallest detectable difference was 0.24 l for algorithm measurements which was similar to manual measurements. Conclusions: This lung segmentation approach provided the necessary and sufficient precision and accuracy required for research and clinical studies.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2016

Deductive Evaluation: Implicit Code Verification With Low User Burden

We describe a framework for symbolically evaluating C code using a deductive approach that discovers and proves program properties. The framework applies Floyd-Hoare verification principles in its treatment of loops, with a library of iteration schemes serving to derive loop invariants. During evaluation, theorem proving is performed on-the-fly, obviating the generation of verification conditions normally needed to establish loop properties. A PVS-based prototype is presented along with results for sample C functions.

Di Vito, Ben L.↗

DOE OSTI2022

Accelerating Noisy VQE Optimization with Gaussian Processes

Hybrid variational quantum algorithms, which combine a classical optimizer with evaluations on a quantum chip, are the most promising candidates to show quantum advantage on current noisy, intermediate-scale quantum (NISQ) devices. The classical optimizer is required to perform well in the presence of noise in the objective function evaluations, or else it becomes the weakest link in the algorithm. We introduce the use of Gaussian Processes (GP) as surrogate models to reduce the impact of noise and to provide high quality seeds to escape local minima, whether real or noise-induced. We build this as a framework on top of local optimizations, for which we choose Implicit Filtering (ImFil) in this study. ImFil is a state-of-the-art, gradient-free method, which in comparative studies has been shown to outperform on noisy VQE problems. The result is a new method: "GP+ImFil". We show that when noise is present, the GP+ImFil approach finds results closer to the true global minimum in fewer evaluations than standalone ImFil, and that it works particularly well for larger dimensional problems. Using GP to seed local searches in a multi-modal landscape shows mixed results: although it is capable of improving on ImFil standalone, it does not do so consistently and would only be preferred over other, more exhaustive, multistart methods if resources are constrained.

Muller, Juliane↗

DOE OSTI2018

High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics

We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below M=10 -5 , which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the AUSM + -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Fast HARDI Uncertainty Quantification and Visualization with Spherical Sampling

In this paper, we study uncertainty quantification and visualization of orientation distribution functions (ODF), which corresponds to the diffusion profile of high angular resolution diffusion imaging (HARDI) data. The shape inclusion probability (SIP) function is the state‐of‐the‐art method for capturing the uncertainty of ODF ensembles. The current method of computing the SIP function with a volumetric basis exhibits high computational and memory costs, which can be a bottleneck to integrating uncertainty into HARDI visualization techniques and tools. We propose a novel spherical sampling framework for faster computation of the SIP function with lower memory usage and increased accuracy. In particular, we propose direct extraction of SIP isosurfaces, which represent confidence intervals indicating spatial uncertainty of HARDI glyphs, by performing spherical sampling of ODFs. Our spherical sampling approach requires much less sampling than the state‐of‐the‐art volume sampling method, thus providing significantly enhanced performance, scalability, and the ability to perform implicit ray tracing. Our experiments demonstrate that the SIP isosurfaces extracted with our spherical sampling approach can achieve up to 8164× speedup, 37282× memory reduction, and 50.2% less SIP isosurface error compared to the classical volume sampling approach. We demonstrate the efficacy of our methods through experiments on synthetic and human‐brain HARDI datasets.

97 MATHEMATICS AND COMPUTING↗