Publications

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As part of the Department of Energy response to the novel coronavirus pandemic of 2020, a modeling effort was sponsored by the DOE Office of Science. One task of this modeling effort at Sandia was to develop a model to predict medical resource needs given various patient arrival scenarios. Resources needed include personnel resources (nurses, ICU nurses, physicians, respiratory therapists), fixed resources (regular or ICU beds and ventilators), and consumable resources (masks, gowns, gloves, face shields, sedatives). This report documents the uncertainty analysis that was performed on the resource model. The uncertainty analysis involved sampling 26 input parameters to the model. The sampling was performed conditional on the patient arrival streams that also were inputs to the model. These patient arrival streams were derived from various epidemiology models and had a significant effect on the projected resource needs. In this report, we document the sampling approach, the parameter ranges used, and the computational workflow necessary to perform large-scale uncertainty studies for every county and state in the United States.

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Graph partitioning has been an important tool to partition the work among several processors to minimize the communication cost and balance the workload. While accelerator-based supercomputers are emerging to be the standard, the use of graph partitioning becomes even more important as applications are rapidly moving to these architectures. However, there is no scalable, distributed-memory, multi-GPU graph partitioner available for applications. We developed a spectral graph partitioner, Sphynx, using the portable, accelerator-friendly stack of the Trilinos framework. We use Sphnyx to systematically evaluate the various algorithmic choices in spectral partitioning with a focus on GPU performance. We perform those evaluations on irregular graphs, because state-of-the-art partitioners have the most difficulty on them. We demonstrate that Sphynx is up to 17x faster on GPUs compared to the case on CPUs, and up to 580x faster compared to a state-of-the-art multilevel partitioner. Sphynx provides a robust alternative for applications looking for a GPU-based partitioner.

A broad set of data science and engineering questions may be organized as graphs, providing a powerful means for describing relational data. Although experts now routinely compute graph algorithms on huge, unstructured graphs using high performance computing (HPC) or cloud resources, this practice hasn't yet broken into the mainstream. Such computations require great expertise, yet users often need rapid prototyping and development to quickly customize existing code. Toward that end, we are exploring the use of the Chapel programming language as a means of making some important graph analytics more accessible, examining the breadth of characteristics that would make for a productive programming environment, one that is expressive, performant, portable, and robust.

Bayesian optimization (BO) is an effective surrogate-based method that has been widely used to optimize simulation-based applications. While the traditional Bayesian optimization approach only applies to single-fidelity models, many realistic applications provide multiple levels of fidelity with various levels of computational complexity and predictive capability. In this work, we propose a multi-fidelity Bayesian optimization method for design applications with both known and unknown constraints. The proposed framework, called sMF-BO-2CoGP, is built on a multi-level CoKriging method to predict the objective function. An external binary classifier, which we approximate using a separate CoKriging model, is used to distinguish between feasible and infeasible regions. Finally, the sMF-BO-2CoGP method is demonstrated using a series of analytical examples and a flip-chip application for design optimization to minimize the deformation due to warping under thermal loading conditions.

We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations. Specifically, we first create a coarse solver by eliminating and/or limiting the front growth in nested dissection. This is accomplished by projecting the trace data into a sequence of same or high-order polynomials on a set of increasingly h-coarser edges/faces. We then combine the coarse solver with a block-Jacobi fine scale solver to form a two-level solver/preconditioner. Numerical experiments indicate that the performance of the resulting two-level solver/preconditioner depends on the smoothness of the solution and can offer significant speedups and memory savings compared to the nested dissection direct solver. While the proposed algorithms are developed within the HDG framework, they are applicable to other hybrid(ized) high-order finite element methods. Moreover, we show that our multilevel algorithms can be interpreted as a multigrid method with specific intergrid transfer and smoothing operators. With several numerical examples from Poisson, pure transport, and convection-diffusion equations we demonstrate the robustness and scalability of the algorithms with respect to solution order. While scalability with mesh size in general is not guaranteed and depends on the smoothness of the solution and the type of equation, improving it is a part of future work.

Here, we study orthogonal polynomials with respect to self-similar measures, focusing on the class of infinite Bernoulli convolutions, which are defined by iterated function systems with overlaps, especially those defined by the Pisot, Garsia, and Salem numbers. By using an algorithm of Mantica, we obtain graphs of the coefficients of the 3-term recursion relation defining the orthogonal polynomials. We use these graphs to predict whether the singular infinite Bernoulli convolutions belong to the Nevai class. Based on our numerical results, we conjecture that all infinite Bernoulli convolutions with contraction ratios greater than or equal to 1/2 belong to Nevai’s class, regardless of the probability weights assigned to the self-similar measures.

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This report describes the results of a seven day effort to assist subject matter experts address a problem related to COVID-19. In the course of this effort, we analyzed the 29K documents provided as part of the White House's call to action. This involved applying a variety of natural language processing techniques and compression-based analytics in combination with visualization techniques and assessment with subject matter experts to pursue answers to a specific question. In this paper, we will describe the algorithms, the software, the study performed, and availability of the software developed during the effort.

Non-volatile memory arrays can deploy pre-trained neural network models for edge inference. However, these systems are affected by device-level noise and retention issues. Here, we examine damage caused by these effects, introduce a mitigation strategy, and demonstrate its use in fabricated array of SONOS (Silicon-Oxide-Nitride-Oxide-Silicon) devices. On MNIST, fashion-MNIST, and CIFAR-10 tasks, our approach increases resilience to synaptic noise and drift. We also show strong performance can be realized with ADCs of 5-8 bits precision.

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The ExaLearn miniGAN team (Ellis and Rajamanickam) have released miniGAN, a generative adversarial network(GAN) proxy application, through the ECP proxy application suite. miniGAN is the first machine learning proxy application in the suite (note: the ECP CANDLE project did previously release some benchmarks) and models the performance for training generator and discriminator networks. The GAN's generator and discriminator generate plausible 2D/3D maps and identify fake maps, respectively. miniGAN aims to be a proxy application for related applications in cosmology (CosmoFlow, ExaGAN) and wind energy (ExaWind). miniGAN has been developed so that optimized mathematical kernels (e.g., kernels provided by Kokkos Kernels) can be plugged into to the proxy application to explore potential performance improvements. miniGAN has been released as open source software and is available through the ECP proxy application website (https://proxyapps.exascaleproject.ordecp-proxy-appssuite/) and on GitHub (https://github.com/SandiaMLMiniApps/miniGAN). As part of this release, a generator is provided to generate a data set (series of images) that are inputs to the proxy application.

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