Publications

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This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.

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This report details work to study trade-offs in topology and network bandwidth for potential interconnects in the exascale (2021-2022) timeframe. The work was done using multiple interconnect models across two parallel discrete event simulators. Results from each independent simulator are shown and discussed and the areas of agreement and disagreement are explored.

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Partial differential equations (PDEs) are used with huge success to model phenomena across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDEs fail to adequately model observed phenomena, or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. Here, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modelling and algorithmic extensions, which serve to show the wide applicability of nonlocal modelling.

In this paper, the magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated by means of spin dynamics simulations coupled to molecular dynamics, using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, going beyond the cluster and bulk Curie temperatures. Comparison is made with experimental data and with theoretical models based on the mean-field Ising model adapted to small clusters, and taking into account the influence of low coordinated spins at free surfaces. Our results for the temperature dependence of the average magnetization per atom M (T), including the thermalization of the transnational lattice degrees of freedom, are in very good agreement with available experimental measurements on small Fe nanoclusters. In contrast, significant discrepancies with experiment are observed if the translational degrees of freedom are artificially frozen. The finite-size effects on M (T) are found to be particularly important near the cluster Curie temperature. Simulated magnetization above the Curie temperature scales with cluster size as predicted by models assuming short-range magnetic ordering. Analytical approximations to the magnetization as a function of temperature and size are proposed.

The use of multiple types of precision in mathematical software has the potential to increase its performance on new heterogeneous architectures. The xSDK project focuses both on the investigation and development of multiprecision algorithms as well as their inclusion into xSDK member libraries. This report summarizes current efforts on including and/or using mixed precision capabilities in the math libraries Ginkgo, heFFTe, hypre, MAGMA, PETSc/TAO, SLATE, SuperLU, and Trilinos, including KokkosKernels. It contains both numerical results from libraries that already provide mixed precision capabilities, as well as descriptions of the strategies to incorporate multiprecision into established libraries.

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Neuromorphic computing is a critical future technology for the computing industry, but it has yet to achieve its promise and has struggled to establish a cohesive research community. A large part of the challenge is that full realization of the potential of brain inspiration requires advances in both device hardware, computing architectures, and algorithms. This simultaneous development across technology scales is unprecedented in the computing field. This article presents a strategy, framed by market and policy pressures, for moving past these current technological and cultural hurdles to realize its full impact across technology. Achieving the full potential of brain-derived algorithms as well as post-complementary metal-oxide-semiconductor (CMOS) scaling neuromorphic hardware requires appropriately balancing the near-term opportunities of deep learning applications with the long-term potential of less understood opportunities in neural computing.

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse structure and the tensor elements are nonnegative count data. SparTen is a high-performance C++ library which computes a low-rank decomposition using different solvers: a first-order quasi-Newton or a second-order damped Newton method, along with the appropriate choice of runtime parameters. Since default parameters in SparTen are tuned to experimental results in prior published work on a single real-world dataset conducted using MATLAB implementations of these methods, it remains unclear if the parameter defaults in SparTen are appropriate for general tensor data. Furthermore, it is unknown how sensitive algorithm convergence is to changes in the input parameter values. This report addresses these unresolved issues with large-scale experimentation on three benchmark tensor data sets. Experiments were conducted on several different CPU architectures and replicated with many initial states to establish generalized profiles of algorithm convergence behavior.

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering continuum models from high fidelity molecular simulation data. Our approach applies a neural network parameterization of governing physics in modal space, allowing a characterization of differential operators while providing structure which may be used to impose biases related to symmetry, isotropy, and conservation form. Here, we demonstrate the effectiveness of our framework for a variety of physics, including local and nonlocal diffusion processes and single and multiphase flows. For the flow physics we demonstrate this approach leads to a learned operator that generalizes to system characteristics not included in the training sets, such as variable particle sizes, densities, and concentration.

Here, we describe recent efforts to improve our predictive modeling of rate-dependent behavior at, or near, a phase transition using molecular dynamics simulations. Cadmium sulfide (CdS) is a well-studied material that undergoes a solid-solid phase transition from wurtzite to rock salt structures between 3 and 9 GPa. Atomistic simulations are used to investigate the dominant transition mechanisms as a function of orientation, size and rate. We found that the final rock salt orientations were determined relative to the initial wurtzite orientation, and that these orientations were different for the two orientations and two pressure regimes studied. The CdS solid-solid phase transition is studied, for both a bulk single crystal and for polymer-encapsulated spherical nanoparticles of various sizes.

Signal arrival-time estimation plays a critical role in a variety of downstream seismic analyses, including location estimation and source characterization. Any arrival-time errors propagate through subsequent data-processing results. In this article, we detail a general framework for refining estimated seismic signal arrival times along with full estimation of their associated uncertainty. Using the standard short-term average/long-term average threshold algorithm to identify a search window, we demonstrate how to refine the pick estimate through two different approaches. In both cases, new waveform realizations are generated through bootstrap algorithms to produce full a posteriori estimates of uncertainty of onset arrival time of the seismic signal. The onset arrival uncertainty estimates provide additional data-derived information from the signal and have the potential to influence seismic analysis along several fronts.

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The Computer Science Research Institute (CSRI) brings university faculty and students to Sandia for focused collaborative research on Department of Energy (DOE) computer and computational science problems. The institute provides an opportunity for university researchers to learn about problems in computer and computational science at DOE laboratories. Participants conduct leading-edge research, interact with scientists and engineers at the laboratories, and help transfer results of their research to programs at the labs. Some specific CSRI research interest areas are: scalable solvers, optimization, adaptivity and mesh refinement, graph-based, discrete, and combinatorial algorithms, uncertainty estimation, mesh generation, dynamic load-balancing, virus and other malicious-code defense, visualization, scalable cluster computers, data-intensive computing, environments for scalable computing, parallel input/output, advanced architectures, and theoretical computer science. The CSRI Summer Program is organized by CSRI and typically includes the organization of a weekly seminar series and the publication of a summer proceedings. In 2020, the CSRI summer program was executed completely virtually; all student interns worked from home, due to the COVID-19 pandemic.

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We develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.

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Graph coloring is often used in parallelizing scientific computations that run in distributed and multi-GPU environments; it identifies sets of independent data that can be updated in parallel. Many algorithms exist for graph coloring on a single GPU or in distributed memory, but hybrid MPI+GPU algorithms have been unexplored until this work, to the best of our knowledge. We present several MPI+GPU coloring approaches that use implementations of the distributed coloring algorithms of Gebremedhin et al. and the shared-memory algorithms of Deveci et al. The on-node parallel coloring uses implementations in KokkosKernels, which provide parallelization for both multicore CPUs and GPUs. We further extend our approaches to solve for distance-2 coloring, giving the first known distributed and multi-GPU algorithm for this problem. In addition, we propose novel methods to reduce communication in distributed graph coloring. Our experiments show that our approaches operate efficiently on inputs too large to fit on a single GPU and scale up to graphs with 76.7 billion edges running on 128 GPUs.

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