SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

We present our recent experience working to design parallel functional control-flow analysis (CFA) using an encoding in Datalog and underlying relational algebra implemented for SIMD coprocessors and supercomputers. Control-flow analysis statically models the possible propagations of data and control through a target program, finitely obtaining a bound on reachable expressions and environments and on possible return and argument values. We used Souffl´e, a parallel CPU-based Datalog implementation from Oracle labs, and worked toward a new MPI-based distributed hash join implementation and an extension of the GPU-based relational algebra library RedFox.

In this paper, we provide introductions to functional flow analysis, Datalog, MPI, and CUDA, explaining the total process we are working on to bring these components together in an analysis pipeline toward the end of scaling functional program analyses by extracting their intrinsic parallelism in a principled manner.

The underlying pathophysiology of ischemia and its electrocardiographic consequences are poorly understood, resulting in unreliable diagnosis of this disease. This limited knowledge of underlying mechanisms suggests a data driven approach, which seeks to identify patterns in the ECG that can be linked statistically to underlying behavior and conditions of ischemic stress. The gold standard ECG metrics for evaluating ischemia monitor vertical deflections within the ST segment. However, ischemia influences all portions of the electrogram. Another metric that targets the QRS complex during ischemia is Conduction Velocity (CV). An even more inclusive, data driven approach is known as "Laplacian Eigenmaps" (LE), which can identify trajectories, or "manifolds", that respond to different spatiotemporal consequences of ischemic stress, and these changes to the trajectories on the manifold may serve as a clinically relevant biomarker. On this study, we compared the LE- and CV-based markers against two gold standards for detecting ischemic stress, both derived from the ST segment. We evaluated the response time and fidelity of each biomarker using a Time to Threshold (TTT) and Contrast Ratio (CR) measure, over 51 episodes recorded as cardiac electrograms from a canine model of controlled ischemia. The results show that metrics designed to monitor regions beyond the ST segment can perform at least as well, if not better, than traditional ST segment based metrics.

The lithiation and delithiation of a silicon battery anode is modeled using the material point method (MPM). The main challenges in modeling this process using the MPM is to simulate stress dependent diffusion coupled with concentration dependent stress within a material that undergoes large deformations. MPM is chosen as the numerical method of choice because of its ability to handle large deformations. A method for modeling diffusion within MPM is described. A stress dependent model for diffusivity and three different constitutive models that fully couple the equations for stress with the equations for diffusion are considered. Verifications tests for the accuracy of the numerical implementations of the models and validation tests with experimental results show the accuracy of the approach. The application of the fully coupled stress diffusion model implemented in MPM is applied to modeling the lithiation and delithiation of silicon nanopillars.

In this work, we discuss the problem of approximating a multivariate function via ℓ1 minimization method, using a random chosen sub-grid of the corresponding tensor grid of Gaussian points. The independent variables of the function are assumed to be random variables, and thus, the framework provides a non-intrusive way to construct the generalized polynomial chaos expansions, stemming from the motivating application of Uncertainty Quantification (UQ). We provide theoretical analysis on the validity of the approach. The framework includes both the bounded measures such as the uniform and the Chebyshev measure, and the unbounded measures which include the Gaussian measure. Several numerical examples are given to confirm the theoretical results.

The University of Utah's Carbon Capture Multidisciplinary Simulation Center (CCMSC) is using the Uintah Computational Framework to predict performance of a 1000 MWe ultra-supercritical clean coal boiler. The center aims to utilize the Intel Xeon Phi-based DOE systems, Theta and Aurora, through the Aurora Early Science Program by using the Kokkos C++ library to enable node-level performance portability. This paper describes infrastructure advancements and portability improvements made possible by our integration of Kokkos within Uintah. Scalability results are presented that compare serial and data parallel task execution models for a challenging radiative heat transfer calculation, central to the center's predictive boiler simulations. These results demonstrate both good strong-scaling characteristics to 256 Knights Landing (KNL) processors on the NSF Stampede system, and show the KNL-based calculation to compete with prior GPU-based results for the same calculation.

In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models subject to uncertain input parameters. The standard sampling approach for recovering sparse polynomials is to use Monte Carlo (MC) sampling of the density of orthogonality. However MC methods result in poor function recovery when the polynomial degree is high. Here we propose a general algorithm that can be applied to any admissible weight function on a bounded domain and a wide class of exponential weight functions defined on unbounded domains. Our proposed algorithm samples with respect to the weighted equilibrium measure of the parametric domain, and subsequently solves a preconditioned ℓ1-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. We present theoretical analysis to motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. Numerical examples are also provided that demonstrate that our proposed Christoffel Sparse Approximation algorithm leads to comparable or improved accuracy even when compared with Legendre and Hermite specific algorithms.

The reduced basis method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the offline portion of the algorithm is a greedy algorithm, requiring maximization of an error estimate over parameter space. In practice this maximization is usually performed by replacing the parameter domain continuum with a discrete "training" set. When the dimension of parameter space is large, it is necessary to significantly increase the size of this training set in order to effectively search parameter space. Large training sets diminish the attractiveness of RBM algorithms since this proportionally increases the cost of the offline phase. In this work we propose novel strategies for offline RBM algorithms that mitigate the computational difficulty of maximizing error estimates over a training set. The main idea is to identify a subset of the training set, a "surrogate training set" (STS), on which to perform greedy algorithms. The STS we construct is much smaller in size than the full training set, yet our examples suggest that it is accurate enough to induce the solution manifold of interest at the current offline RBM iteration. We propose two algorithms to construct the STS: our first algorithm, the successive maximization method, is inspired by inverse transform sampling for non-standard univariate probability distributions. The second constructs an STS by identifying pivots in the Cholesky decomposition of an approximate error correlation matrix. We demonstrate the algorithm through numerical experiments, showing that it is capable of accelerating offline RBM procedures without degrading accuracy, assuming that the solution manifold has rapidly decaying Kolmogorov width.

Background:
With ever-increasing amounts of data produced in biology research, scientists are in need of efficient data analysis methods. Cluster analysis, combined with visualization of the results, is one such method that can be used to make sense of large data volumes. At the same time, cluster analysis is known to be imperfect and depends on the choice of algorithms, parameters, and distance measures. Most clustering algorithms don't properly account for ambiguity in the source data, as records are often assigned to discrete clusters, even if an assignment is unclear. While there are metrics and visualization techniques that allow analysts to compare clusterings or to judge cluster quality, there is no comprehensive method that allows analysts to evaluate, compare, and refine cluster assignments based on the source data, derived scores, and contextual data.

Results:
In this paper, we introduce a method that explicitly visualizes the quality of cluster assignments, allows comparisons of clustering results and enables analysts to manually curate and refine cluster assignments. Our methods are applicable to matrix data clustered with partitional, hierarchical, and fuzzy clustering algorithms. Furthermore, we enable analysts to explore clustering results in context of other data, for example, to observe whether a clustering of genomic data results in a meaningful differentiation in phenotypes.

Conclusions:
Our methods are integrated into Caleydo StratomeX, a popular, web-based, disease subtype analysis tool. We show in a usage scenario that our approach can reveal ambiguities in cluster assignments and produce improved clusterings that better differentiate genotypes and phenotypes.

Hierarchical data representations have been shown to be effective tools for coping with large-scale scientific data. Writing hierarchical data on supercomputers, however, is challenging as it often involves all-to-one communication during aggregation of low-resolution data which tends to span the entire network domain, resulting in several bottlenecks. We introduce the concept of indexing templates, which succinctly describe data organization and can be used to alter movement of data in beneficial ways. We present two techniques, domain partitioning and localized aggregation, that leverage indexing templates to alleviate congestion and synchronization overheads during data aggregation. We report experimental results that show significant I/O speedup using our proposed schemes on two of today's fastest supercomputers, Mira and Shaheen II, using the Uintah and S3D simulation frameworks.

Hierarchical data representations have been shown to be effective tools for coping with large-scale scientific data. Writing hierarchical data on supercomputers, however, is challenging as it often involves all-to-one communication during aggregation of low-resolution data which tends to span the entire network domain, resulting in several bottlenecks. We introduce the concept of indexing templates, which succinctly describe data organization and can be used to alter movement of data in beneficial ways. We present two techniques, domain partitioning and localized aggregation, that leverage indexing templates to alleviate congestion and synchronization overheads during data aggregation. We report experimental results that show significant I/O speedup using our proposed schemes on two of today's fastest supercomputers, Mira and Shaheen II, using the Uintah and S3D simulation frameworks.

For visualization pedagogy, an important but challenging notion to teach is design, from making to evaluating visualization encodings, user interactions, or data visualization systems. In our previous work, we introduced the design activity framework to codify the high-level activities of the visualization design process. This framework has helped structure experts' design processes to create visualization systems, but the framework's four activities lack a breakdown into steps with a concrete example to help novices utilizing this framework in their own real-world design process. To provide students with such concrete guidelines, we created worksheets for each design activity: understand, ideate, make, and deploy. Each worksheet presents a high-level summary of the activity with actionable, guided steps for a novice designer to follow. We validated the use of this framework and the worksheets in a graduate-level visualization course taught at our university. For this evaluation, we surveyed the class and conducted 13 student interviews to garner qualitative, open-ended feedback and suggestions on the worksheets. We conclude this work with a discussion and highlight various areas for future work on improving visualization design pedagogy.

Discontinuous Galerkin (DG) methods are a popular class of numerical techniques to solve partial differential equations due to their higher order of accuracy. However, the inter-element discontinuity of a DG solution hinders its utility in various applications, including visualization and feature extraction. This shortcoming can be alleviated by postprocessing of DG solutions to increase the inter-element smoothness. A class of postprocessing techniques proposed to increase the inter-element smoothness is SIAC filtering. In addition to increasing the inter-element continuity, SIAC filtering also raises the convergence rate from order k+1 to order 2k+1. Since the introduction of SIAC filtering for univariate hyperbolic equations by Cockburn et al. (Math Comput 72(242):577–606, 2003), many generalizations of SIAC filtering have been proposed. Recently, the idea of dimensionality reduction through rotation has been the focus of studies in which a univariate SIAC kernel has been used to postprocess a two-dimensional DG solution (Docampo-Sánchez et al. in Multi-dimensional filtering: reducing the dimension through rotation, 2016. arXiv preprint arXiv:1610.02317). However, the scope of theoretical development of multidimensional SIAC filters has never gone beyond the usage of tensor product multidimensional B-splines or the reduction of the filter dimension. In this paper, we define a new SIAC filter called hexagonal SIAC (HSIAC) that uses a nonseparable class of two-dimensional spline functions called hex splines. In addition to relaxing the separability assumption, the proposed HSIAC filter provides more symmetry to its tensor-product counterpart. We prove that the superconvergence property holds for a specific class of structured triangular meshes using HSIAC filtering and provide numerical results to demonstrate and validate our theoretical results.

Heterogeneous data pose serious challenges to data analysis tasks, including exploration and visualization. Current techniques often utilize dimensionality reductions, aggregation, or conversion to numerical values to analyze heterogeneous data. However, the effectiveness of such techniques to find subtle structures such as the presence of multiple modes or detection of outliers is hindered by the challenge to find the proper subspaces or prior knowledge to reveal the structures. In this paper, we propose a generic similarity-based exploration technique that is applicable to a wide variety of datatypes and their combinations, including heterogeneous ensembles. The proposed concept of similarity has a close connection to statistical analysis and can be deployed for summarization, revealing fine structures such as the presence of multiple modes, and detection of anomalies or outliers. We then propose a visual encoding framework that enables the exploration of a heterogeneous dataset in different levels of detail and provides insightful information about both global and local structures. We demonstrate the utility of the proposed technique using various real datasets, including ensemble data.

We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame- work. Our method is motivated by generalized Polynomial Chaos approximation in uncertainty quantification where a polynomial approximation is formed from a combination of orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density of orthogonality. Our proposed algorithm samples with respect to the equilibrium measure of the parametric domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis to motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.

Parallel code portability in the petascale era requires modifying existing codes to support new architectures with large core counts and SIMD vector units. OpenMP is a well established and increasingly supported vehicle for portable parallelization. As architectures mature and compiler OpenMP implementations evolve, best practices for code modernization change as well. In this paper, we examine the impact of newer OpenMP features (in particular OMP SIMD) on the Intel Xeon Phi Knights Landing (KNL) architecture, applied in optimizing loops in the single moment 6-class microphysics module (WSM6) in the US Navy's NEPTUNE code. We find that with functioning OMP SIMD constructs, low thread invocation overhead on KNL and reduced penalty for unaligned access compared to previous architectures, one can leverage OpenMP 4 to achieve reasonable scalability with relatively minor reorganization of a production physics code.

Optimizations in the petascale era require modifications of existing codes to take advantage of new architectures with large core counts and SIMD vector units. This paper examines high-level and low-level optimization strategies for numerical weather prediction (NWP) codes. These strategies employ thread-local structures of arrays (SOA) and an OpenMP directive such as OMP SIMD. These optimization approaches are applied to the Weather Research Forecasting single-moment 6-class microphysics schemes (WSM6) in the US Navy NEPTUNE system. The results of this study indicate that the high-level approach with SOA and low-level OMP SIMD improves thread and vector parallelism by increasing data and temporal locality. The modified version of WSM6 runs 70x faster than the original serial code. This improvement is about 23.3x faster than the performance achieved by Ouermi et al., and 14.9x faster than the performance achieved by Michalakes et al.

A large body of evidence relates autism with abnormal structural and functional brain connectivity. Structural covariance MRI (scMRI) is a technique that maps brain regions with covarying gray matter density across subjects. It provides a way to probe the anatomical structures underlying intrinsic connectivity networks (ICNs) through the analysis of the gray matter signal covariance. In this paper, we apply topological data analysis in conjunction with scMRI to explore network-specific differences in the gray matter structure in subjects with autism versus age-, gender- and IQ-matched controls. Specifically, we investigate topological differences in gray matter structures captured by structural covariance networks (SCNs) derived from three ICNs strongly implicated in autism, namely, the salience network (SN), the default mode network (DMN) and the executive control network (ECN). By combining topological data analysis with statistical inference, our results provide evidence of statistically significant network-specific structural abnormalities in autism, from SCNs derived from SN and ECN. These differences in brain architecture are consistent with direct structural analysis using scMRI (Zielinski et al. 2012).

Large-scale parallel applications with complex global data dependencies beyond those of reductions pose significant scalability challenges in an asynchronous runtime system. Internodal challenges include identifying the all-to-all communication of data dependencies among the nodes. Intranodal challenges include gathering together these data dependencies into usable data objects while avoiding data duplication. This paper addresses these challenges within the context of a large-scale, industrial coal boiler simulation using the Uintah asynchronous many-task runtime system on GPU architectures. We show significant reduction in time spent analyzing data dependencies through refinements in our dependency search algorithm. Multiple task graphs are used to eliminate subsequent analysis when task graphs change in predictable and repeatable ways. Using a combined data store and task scheduler redesign reduces data dependency duplication ensuring that problems fit within host and GPU memory. These modifications did not require any changes to application code or sweeping changes to the Uintah runtime system. We report results running on the DOE Titan system on 119K CPU cores and 7.5K GPUs simultaneously. Our solutions can be generalized to other task dependency problems with global dependencies among thousands of nodes which must be processed efficiently at large scale.

Modern science is inundated with ever increasing data sizes as computational capabilities and image acquisition techniques continue to improve. For example, simulations are tackling ever larger domains with higher fidelity, and high-throughput microscopy techniques generate larger data that are fundamental to gather biologically and medically relevant insights. As the image sizes exceed memory, and even sometimes local disk space, each step in a scientific workflow is impacted. Current software solutions enable data exploration with limited interactivity for visualization and analytic tasks. Furthermore analysis on HPC systems often require complex hand-written parallel implementations of algorithms that suffer from poor portability and maintainability. We present a software infrastructure that simplifies end-to-end visualization and analysis of massive data. First, a hierarchical streaming data access layer enables interactive exploration of remote data, with fast data fetching to test analytics on subsets of the data. Second, a library simplifies the process of developing new analytics algorithms, allowing users to rapidly prototype new approaches and deploy them in an HPC setting. Third, a scalable runtime system automates mapping analysis algorithms to whatever computational hardware is available, reducing the complexity of developing scaling algorithms. We demonstrate the usability and performance of our system using a use case from neuroscience: filtering, registration, and visualization of tera-scale microscopy data. We evaluate the performance of our system using a leadership-class supercomputer, Shaheen II.

This article surveys the history and current state of the art of visualization in meteorology, focusing on visualization techniques and tools used for meteorological data analysis. We examine characteristics of meteorological data and analysis tasks, describe the development of computer graphics methods for visualization in meteorology from the 1960s to today, and visit the state of the art of visualization techniques and tools in operational weather forecasting and atmospheric research. We approach the topic from both the visualization and the meteorological side, showing visualization techniques commonly used in meteorological practice, and surveying recent studies in visualization research aimed at meteorological applications. Our overview covers visualization techniques from the fields of display design, 3D visualization, flow dynamics, feature-based visualization, comparative visualization and data fusion, uncertainty and ensemble visualization, interactive visual analysis, efficient rendering, and scalability and reproducibility. We discuss demands and challenges for visualization research targeting meteorological data analysis, highlighting aspects in demonstration of benefit, interactive visual analysis, seamless visualization, ensemble visualization, 3D visualization, and technical issues.