Publications

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This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

Supported by the U.S. Department of Energy (DOE), the Energy Exascale Earth System Model (E3SM) project aims to optimize the use of DOE resources to address the grand challenge of actionable predictions of Earth system variability and change. This requires sustained advancement to (1) integrate model development with leading-edge computational advances toward ultra-high-resolution modeling; (2) represent the coupled human-Earth system to address energy sector vulnerability to variability and change; and (3) address uncertainty in model simulations and projections. Scientific development of the E3SM modeling system is driven by the simulation requirements in three overarching science areas centering on understanding the Earth's water cycle, biogeochemistry, and cryosphere systems and their future changes. This paper serves as an introduction to the E3SM special collection, which includes 50 papers published in several AGU journals. It provides an overview of the E3SM project, including its goals and science drivers. It also provides a brief history of the development of E3SM version 1 and highlights some key findings from papers included in the special collection.

Performance variation deriving from hardware and software sources is common in modern scientific and data-intensive computing systems, and synchronization in parallel and distributed programs often exacerbates their impacts at scale. The decentralized and emergent effects of such variation are, unfortunately, also difficult to systematically measure, analyze, and predict; modeling assumptions which are stringent enough to make analysis tractable frequently cannot be guaranteed at meaningful application scales, and longitudinal methods at such scales can require the capture and manipulation of impractically large amounts of data. This paper describes a new, scalable, and statistically robust approach for effective modeling, measurement, and analysis of large-scale performance variation in HPC systems. Our approach avoids the need to reason about complex distributions of runtimes among large numbers of individual application processes by focusing instead on the maximum length of distributed workload intervals. We describe this approach and its implementation in MPI which makes it applicable to a diverse set of HPC workloads. We also present evaluations of these techniques for quantifying and predicting performance variation carried out on large-scale computing systems, and discuss the strengths and limitations of the underlying modeling assumptions.

We present an effort to port the nonhydrostatic atmosphere dynamical core of the Energy Exascale Earth System Model (E3SM) to efficiently run on a variety of architectures, including conventional CPU, many-core CPU, and GPU. We specifically target cloud-resolving resolutions of 3 km and 1 km. To express on-node parallelism we use the C++ library Kokkos, which allows us to achieve a performance portable code in a largely architecture-independent way. Our C++ implementation is at least as fast as the original Fortran implementation on IBM Power9 and Intel Knights Landing processors, proving that the code refactor did not compromise the efficiency on CPU architectures. On the other hand, when using the GPUs, our implementation is able to achieve 0.97 Simulated Years Per Day, running on the full Summit supercomputer. To the best of our knowledge, this is the most achieved to date by any global atmosphere dynamical core running at such resolutions.

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The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind simulation environment are Nalu-Wind, an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, AMR-Wind, a block-structured-grid solver with adaptive mesh refinement capabilities, and OpenFAST, a wind-turbine structural dynamics solver. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and Helmholtz-type equations for transport of momentum and other scalars. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. The choice of overset-mesh methodology to model the moving and non-moving parts of the computational domain introduces constraint equations in the elliptic pressure-Poisson solver. The presence of constraints greatly affects the performance of algebraic multigrid preconditioners.

A memo concerning the status of the Exascale Computing Project (ECP) STDA05-54 is given.

In this paper, we present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the local and nonlocal problem domains, and the virtual controls are the nonlocal volume constraint and the local boundary condition. We present the method in the context of Local-to-Nonlocal di usion coupling. Numerical examples illustrate the theoretical properties of the approach.

Using a numerical ice flow model, we study changes in ice shelf buttressing and grounding-line flux due to localized ice thickness perturbations, a proxy for localized changes in sub-ice-shelf melting. From our experiments, applied to idealized (MISMIPC) and realistic (Larsen C) ice shelf domains, we identify a correlation between a locally derived buttressing number on the ice shelf, based on the first principal stress, and changes in the integrated grounding-line flux. The origin of this correlation, however, remains elusive from the perspective of a theoretical or physically based understanding. This and the fact that the correlation is generally much poorer when applied to realistic ice shelf domains motivate us to seek an alternative approach for predicting changes in grounding-line flux.We therefore propose an adjoint-based method for calculating the sensitivity of the integrated grounding-line flux to local changes in ice shelf geometry. We show that the adjoint-based sensitivity is identical to that deduced from pointwise, diagnostic model perturbation experiments. Based on its much wider applicability and the significant computational savings, we propose that the adjoint-based method is ideally suited for assessing grounding-line flux sensitivity to changes in sub-ice-shelf melting.

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a larger effort in scientific machine learning, many recent works have incorporated physical constraints or other a priori information within Gaussian process regression to supplement limited data and regularize the behavior of the model. We provide an overview and survey of several classes of Gaussian process constraints, including positivity or bound constraints, monotonicity and convexity constraints, differential equation constraints provided by linear PDEs, and boundary condition constraints. We compare the strategies behind each approach as well as the differences in implementation, concluding with a discussion of the computational challenges introduced by constraints.

The lack of a reliable method to evaluate the convergence of molecular dynamics simulations has contributed to discrepancies in different areas of molecular dynamics. In the present work, the method of information entropy is introduced to molecular dynamics for stationarity assessment. The Shannon information entropy formalism is used to monitor the convergence of the atom motion to a steady state in a continuous spatial domain and is also used to assess the stationarity of calculated multidimensional fields such as the temperature field in a discrete spatial domain. It is demonstrated in this work that monitoring the information entropy of the atom position matrix provides a clear indicator of reaching steady state in radiation damage simulations, non-equilibrium molecular dynamics thermal conductivity computations, and simulations of Poiseuille and Couette flow in nanochannels. A main advantage of the present technique is that it is non-local and relies on fundamental quantities available in all molecular dynamics simulations. Unlike monitoring average temperature, the technique is applicable to simulations that conserve total energy such as reverse non-equilibrium molecular dynamics thermal conductivity computations and to simulations where energy dissipates through a boundary as in radiation damage simulations. The method is applied to simulations of iron using the Tersoff/ZBL splined potential, silicon using the Stillinger-Weber potential, and to Lennard-Jones fluid. Its applicability to both solids and fluids shows that the technique has potential for generalization to other areas in molecular dynamics.

Not long ago, it was shown that a discrete time crystal can be realized if a quantum system is periodically driven to a non-equilibrium state. Proof-of-concept experiments are reported by two groups using trapped ions and nitrogen-vacancy centers in diamond, respectively. The concept of discrete time crystals vividly demonstrates that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium. In this project, we want to test this novel concept in another canonical quantum system, the quantum Hall system in a two-dimensional electron gas (2DEG). Compared to other systems, quantum Hall magnetism (QHM) in high quality, industry-compatible GaAs/AlGaAs heterostructures allows for detailed and quantitative studies in a particularly simple and clean environment. This detailed knowledge should help achieve longer coherence times in a driven QHM system. This report will detail the results from a recent study on the stability of the quantum Hall skyrmions (QHS) state at a Landau level filling close to ν = 1 by measuring its current-voltage (I-V) breakdown characteristics under radio-frequency (RF) radiations. We observe that the critical current increases visibly when the RF frequency is right at the Larmor frequency of 75As nuclei, where the hyperfine interaction between electron and nuclear spins perturbs the QHS state most significantly. We believe that this observation is consistent with the novel concept that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium.

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In this report we investigate the utility of one-dimensional convolutional neural network (CNN) models in epidemiological forecasting. Deep learning models, especially variants of recurrent neural networks (RNNs) have been studied for influenza forecasting, and have achieved higher forecasting skill compared to conventional models such as ARIMA models. In this study, we adapt two neural networks that employ one-dimensional temporal convolutional layers as a primary building block temporal convolutional networks and simple neural attentive meta-learner for epidemiological forecasting and test them with influenza data from the US collected over 2010-2019. We find that epidemiological forecasting with CNNs is feasible, and their forecasting skill is comparable to, and at times, superior to, RNNs. Thus CNNs and RNNs bring the power of nonlinear transformations to purely data-driven epidemiological models, a capability that heretofore has been limited to more elaborate mechanistic/compartmental disease models.

Triangle counting is a fundamental building block in graph algorithms. In this paper, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

Bigger is often said to be better, and the newest extreme-scale computers certainly are bigger, with millions of processing units. Moreover, the breadth of science performed on the U.S. Department of Energy (DOE) computing facilities is expanding, with new technology such as artificial intelligence emerging. These advances are exciting, creating new opportunities for scientific discovery; however, they also raise new questions for scientists who want to exploit these advances for tackling more complex problems. Will my simulation code be able to utilize the accelerators in extreme-scale computing systems? Can I take advantage of the deepening memory hierarchy in heterogeneous processors? Is there a way around bottlenecks caused by the widening ratio of peak floating-point operations per second to I/0 bandwidth? How can I manage my huge amounts of data effectively? Can I analyze data in situ, or must I transfer it to offline storage for later analysis? To address such questions, DOE announced that it is providing $57.5 million over the next five years for two multidisciplinary teams — FASTMath and RAPIDS2 — to develop new tools and techniques to harness supercomputers for scientific discovery. The teams, called SciDAC Institutes, are part of the Scientific Discovery through Advanced Computing program.

The Spent Fuel and Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and highlevel nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for evaluating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2020 advances of the Geologic Disposal Safety Assessment (GDSA) Framework and PFLOTRAN development groups of the SFWST Campaign. The common mission of these groups is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of disposal options and generic sites. The capability is a framework called GDSA Framework that employs high-performance computing (HPC) capable codes PFLOTRAN and Dakota.

TChem is an open source software library for solving complex computational chemistry problems and analyzing detailed chemical kinetic models. The software provides support for: complex kinetic models for gas-phase and surface chemistry; thermodynamic properties based on NASA polynomials; species production/consumption rates; stable time integrator for solving stiff time ordinary differential equations; and, reactor models such as homogenous gas-phase ignition (with analytical Jacobian matrices), continuously stirred tank reactor, plug-flow reactor. This toolkit builds upon earlier versions that were written in C and featured tools for gas-phase chemistry only. The current version of the software was completely refactored in C++, uses an object-oriented programming model, and adopts Kokkos as its portability layer to make it ready for the next generation computing architectures i.e., multi/many core computing platforms with GPU accelerators. We have expanded the range of kinetic models to include surface chemistry and have added examples pertaining to Continuously Stirred Tank Reactors (CSTR) and Plug Flow Reactor (PFR) models to complement the homogenous ignition examples present in the earlier versions. To exploit the massive parallelism available from modern computing platforms, the current software interface is designed to evaluate samples in parallel, which enables large scale parametric studies, e.g. for sensitivity analysis and model calibration.

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. The resulting method has been successfully applied to steady and transient problems with complex shock patterns. Numerical experiments show that it is able to provide sharp and well resolved shocks. The importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart. Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems. In the case of transient problem, we also observe a reduction in the computational cost.

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The field of visualization encompasses a wide range of techniques, from infographics to isosurfaces. An important subfield called "scientific visualization" is specifically dedicated to data sets with spatial components, i.e., (X, Y, Z) locations. Furthermore, this subfield's name is inspired by the fact that the data in question often come from the sciences, i.e., physics simulations or sensor networks.