Parallel In Time for a Fully Space-Time Adaptive Mesh Refinement Algorithm
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Mathematics and Computing↗
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Building Halo Merger Trees from the Q Continuum Simulation
Cosmological N-body simulations rank among the most computationally intensive efforts today. A key challenge is the analysis of structure, substructure, and the merger history for many billions of compact particle clusters, called halos. Effectively representing the merging history of halos is essential for many galaxy formation models used to generate synthetic sky catalogs, an important application of modern cosmological simulations. Generating realistic mock catalogs requires computing the halo formation history from simulations with large volumes and billions of halos over many time steps, taking hundreds of terabytes of analysis data. We present fast parallel algorithms for producing halo merger trees and tracking halo substructure from a single-level, density-based clustering algorithm. Merger trees are created from analyzing the halo-particle membership function in adjacent snapshots, and substructure is identified by tracking the "cores" of merging halos - sets of particles near the halo center. Core tracking is performed after creating merger trees and uses the relationships found during tree construction to associate substructures with hosts. The algorithms are implemented with MPI and evaluated on a Cray XK7 supercomputer using up to 16,384 processes on data from HACC, a modern cosmological simulation framework. We present results for creating merger trees from 101 analysis snapshots taken from the Q Continuum, a large volume, high mass resolution, cosmological simulation evolving half a trillion particles.
79 ASTRONOMY AND ASTROPHYSICS↗
dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport
DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in an intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.
42 ENGINEERING↗
Scalable quantum computational science: A perspective from block-encodings and polynomial transformations
Significant developments made in quantum hardware and error correction recently have been driving quantum computing toward practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented, including the construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this perspective serves as a gentle introduction to state-of-the-art quantum algorithms for the computational science community and inspires future development of scalable quantum computational science methodologies that bridge theory and practice.
Bayesian inference↗
Parallel Time Integration for Constrained Optimization
The number of transistors in an average processor continues to increase, but individual clock speeds have plateaued. Those transistors are instead going into additional cores, increasing the number of different things that a processor can do at once and placing an emphasis on parallel computation. Many problems in scientific computing follow a time-evolution model, and it can be difficult to solve such problems in parallel across the temporal domain. The Multi-Grid Reduction In Time (MGRIT) algorithm, developed at Lawrence Livermore National Laboratory (LLNL), solves differential equations with a method designed specifically to take advantage of extreme numbers of processors by parallelizing across time. The Tri-diagonal MGRIT (TriMGRIT) algorithm, also developed at LLNL, is a generalization of MGRIT which enables parallel-in-time solving of a greater number of problems. Constrained optimization problems, in particular, may be solved in parallel using TriMGRIT. These consist of choosing a control function such that an objective functional is minimized, constrained by a differential-equation. We consider two such problems: applying torque to a pendulum to bring it to a gentle stop and moving a crowd of people from one distribution into another. We also perform some miscellaneous theoretical and practical research, including investigating the use of a line-search subroutine to refine intermediate TriMGRIT results and preliminary work on strategies for choosing operators for TriMGRIT to use.
97 MATHEMATICS AND COMPUTING↗
Collaborative Project: Building improved optimized parameter estimation algorithms to improve methane and nitrogen fluxes in a climate model
Soils in natural and managed ecosystems and wetlands are well known sources of methane, nitrous oxides, and reactive nitrogen gases, but the magnitudes of gas flux to the atmosphere are still poorly constrained. Thus, the reasons for the large increases in atmospheric concentrations of methane and nitrous oxide since the preindustrial time period are not well understood. The low atmospheric concentrations of methane and nitrous oxide, despite being more potent greenhouse gases than carbon dioxide, complicate empirical studies to provide explanations. In addition to climate concerns, the emissions of reactive nitrogen gases from soils are important to the changing nitrogen balance in the earth system, subject to human management, and may change substantially in the future. Thus improved modeling of the emission fluxes of these species from the land surface is important. Currently, there are emission modules for methane and some nitrogen species in the Community Earth System Model’s Community Land Model (CLM-ME/N); however, there are large uncertainties and problems in the simulations, resulting in coarse estimates. In this proposal, we seek to improve these emission modules by combining state-of-the-art process modules for emissions, available data, and new optimization methods. In earth science problems, we often have substantial data and knowledge of processes in disparate systems, and thus we need to combine data and a general process level understanding into a model for projections of future climate that are as accurate as possible. The best methodologies for optimization of parameters in earth system models are still being developed. In this proposal we will develop and apply surrogate algorithms that a) were especially developed for computationally expensive simulations like CLM-ME/N models; b) were (in the earlier surrogate optimization Stochastic RBF) demonstrated to perform very well on computationally expensive complex partial differential equations in earth science with limited numbers of simulations; and, c) will be (as part of the proposed research) significantly improved both by adding asynchronous parallelism, early truncation of unsuccessful simulations, and the improvement of both serial and parallel performance by the use of derivative and sensitivity information from global and local surrogate approximations S(x) . The algorithm development and testing will be focused on the CLM-ME/N model application, but the methods are general and are expected to also perform well on optimization for parameter estimation of other climate models and other classes of continuous multimodal optimization problems arising from complex simulation models. In addition, this proposal will compile available datasets of emissions of methane, nitrous oxides and reactive nitrogen species and develop protocols for site level comparisons with the CLM-ME/N. Once the model parameters are optimized against site level data, the model will be simulated at the global level and compared to atmospheric concentration measurements for the current climate, and future emissions will be estimated using climate change as simulated by the CESM. This proposal combines experts in earth system modeling, optimization, computer science, and process level understanding of soil gas emissions in an interdisciplinary team in order to improve the modeling of methane and nitrogen gas emissions. This proposal thus meets the requirements of the SciDAC RFP, by integrating state-of-the-art computer science and earth system to build an improved earth system model.
54 ENVIRONMENTAL SCIENCES↗
Asynchronous Truncated Multigrid-Reduction-in-Time
In this paper, we present the new “asynchronous truncated multigrid-reduction-in-time” (AT-MGRIT) algorithm for introducing time parallelism to the solution of discretized time-dependent problems. The new algorithm is based on the multigrid-reduction-in-time (MGRIT) approach, which, in certain settings, is equivalent to another common multilevel parallel-in-time method, Parareal. In contrast to Parareal and MGRIT that both consider a global temporal grid over the entire time interval on the coarsest level, the AT-MGRIT algorithm uses truncated local time grids on the coarsest level, each grid covering certain temporal subintervals. Further, these local grids can be solved completely in an independent way from each other, which reduces the sequential part of the algorithm and, thus, increases parallelism in the method. Here, we study the effect of using truncated local coarse grids on the convergence of the algorithm, both theoretically and numerically, and show, using challenging nonlinear problems, that the new algorithm consistently outperforms classical Parareal/MGRIT in terms of time to solution.
97 MATHEMATICS AND COMPUTING↗
Direct simulation Monte Carlo on petaflop supercomputers and beyond
The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief concern to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method’s inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird’s 1994 formulation. In this work, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We highlight a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.
97 MATHEMATICS AND COMPUTING↗
Computing the QRPA level density with the finite amplitude method
Here, we describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Avatar Tools
Supervised machine learning is the process of using past experience to predict the future. "Ensembles" are a machine-learning meta-method that can be applied to most machine learning algorithms. Ensembles generally greatly improve accuracy, reduce or remove most of the design issues presented by machine learning, and are admirably suited to parallel and distributed computation. The Avatar Tools codes are an implementation of ensembles specifically for decision trees. Some features that distinguish Avatar Tools from other "ensembles for decision trees" codes are: (1) Does the bookkeeping necessary for out of bag (OOB) validation. (2) Can use OOB validation to automatically determine optimal ensemble size. (3) Provides an MPI-based parallel implementation, for distributed operation. (4) Provides convenient tools for cross-validation, to assess the accuracy provided by a training set. SAND2020-3858 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Siefert, Christopher↗
CSRI Summer Proceedings 2020
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.
97 MATHEMATICS AND COMPUTING↗
Mr. Scan: extreme scale density-based clustering using a tree-based network of GPGPU nodes, In: SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Density-based clustering algorithms are a widely-used class of data mining techniques that can find irregularly shaped clusters and cluster data without prior knowledge of the number of clusters it contains. DBSCAN is the most well-known density-based clustering algorithm. We introduce our version of DBSCAN, called Mr. Scan, which uses a hybrid parallel implementation that combines the MRNet tree-based distribution network with GPGPU-equipped nodes. Mr. Scan avoids the problems of existing implementations by effectively partitioning the point space and by optimizing DBSCAN's computation over dense data regions. We tested Mr. Scan on both a geolocated Twitter dataset and image data obtained from the Sloan Digital Sky Survey. At its largest scale, Mr. Scan clustered 6.5 billion points from the Twitter dataset on 8,192 GPU nodes on Cray Titan in 17.3 minutes. All other parallel DBSCAN implementations have only demonstrated the ability to cluster up to 100 million points.
Computer Science↗
ExTreeM: Scalable Augmented Merge Tree Computation via Extremum Graphs
Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. Here, this paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph G of an input scalar field f defined on a cell complex K, and subsequently compute the unaugmented merge tree of f on G instead of K; which are equivalent. Any merge tree algorithm can be carried out significantly faster on G, since K in general contains substantially more cells than G. To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of K, can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with high parallel efficiency, and we provide a formal proof of its correctness. Our experiments, performed on publicly available datasets, report a speedup of up to one order of magnitude over the state-of-the-art algorithms included in the TTK and VTK-m software libraries, while also requiring significantly less memory and exhibiting excellent scaling behavior.
97 MATHEMATICS AND COMPUTING↗
2016 KIVA-hpFE Development. A Robust and Accurate Engine Modeling Software
Everything we are doing in R&D is to develop methods and a code for robust, accurate and efficient algorithms in a Parallel (MPI) Modular Object-Oriented code for Industry and Researchers.
97 MATHEMATICS AND COMPUTING↗
Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.
97 MATHEMATICS AND COMPUTING↗
An efficient MPI/OpenMP parallelization of the Hartree–Fock–Roothaan method for the first generation of Intel® Xeon Phi™ processor architecture
The Hartree-Fock (HF) method in the quantum chemistry package GAMESS represents one of the most irregular algorithms in computation today. Major steps in the calculation are the irregular computation of electron repulsion integrals (ERIs) and the building of the Fock matrix. These are the central components of the main Self Consistent Field (SCF) loop, the key hotspot in Electronic Structure (ES) codes. By threading the MPI ranks in the official release of the GAMESS code, we not only speed up the main SCF loop (4x to 6x for large systems), but also achieve a significant (>2x) reduction in the overall memory footprint. These improvements are a direct consequence of memory access optimizations within the MPI ranks. We benchmark our implementation against the official release of the GAMESS code on the Intel R Xeon PhiTM supercomputer. Here, scaling numbers are reported on up to 7,680 cores on Intel Xeon Phi coprocessors.
97 MATHEMATICS AND COMPUTING↗
Efficient Delaunay Tessellation through K-D Tree Decomposition
Delaunay tessellations are fundamental data structures in computational geometry. They are important in data analysis, where they can represent the geometry of a point set or approximate its density. The algorithms for computing these tessellations at scale perform poorly when the input data is unbalanced. We investigate the use of k-d trees to evenly distribute points among processes and compare two strategies for picking split points between domain regions. Because resulting point distributions no longer satisfy the assumptions of existing parallel Delaunay algorithms, we develop a new parallel algorithm that adapts to its input and prove its correctness. We evaluate the new algorithm using two late-stage cosmology datasets. The new running times are up to 50 times faster using k-d tree compared with regular grid decomposition. Moreover, in the unbalanced data sets, decomposing the domain into a k-d tree is up to five times faster than decomposing it into a regular grid.
Morozov, Dmitriy↗
CHOLLA: A NEW MASSIVELY PARALLEL HYDRODYNAMICS CODE FOR ASTROPHYSICAL SIMULATION
We present Computational Hydrodynamics On ParaLLel Architectures (Cholla ), a new three-dimensional hydrodynamics code that harnesses the power of graphics processing units (GPUs) to accelerate astrophysical simulations. Cholla models the Euler equations on a static mesh using state-of-the-art techniques, including the unsplit Corner Transport Upwind algorithm, a variety of exact and approximate Riemann solvers, and multiple spatial reconstruction techniques including the piecewise parabolic method (PPM). Using GPUs, Cholla evolves the fluid properties of thousands of cells simultaneously and can update over 10 million cells per GPU-second while using an exact Riemann solver and PPM reconstruction. Owing to the massively parallel architecture of GPUs and the design of the Cholla code, astrophysical simulations with physically interesting grid resolutions (≳256{sup 3}) can easily be computed on a single device. We use the Message Passing Interface library to extend calculations onto multiple devices and demonstrate nearly ideal scaling beyond 64 GPUs. A suite of test problems highlights the physical accuracy of our modeling and provides a useful comparison to other codes. We then use Cholla to simulate the interaction of a shock wave with a gas cloud in the interstellar medium, showing that the evolution of the cloud is highly dependent on its density structure. We reconcile the computed mixing time of a turbulent cloud with a realistic density distribution destroyed by a strong shock with the existing analytic theory for spherical cloud destruction by describing the system in terms of its median gas density.
79 ASTRONOMY AND ASTROPHYSICS↗