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DOE OSTI2017

AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids

We present an augmented matrix approach to update the solution to a linear system of equations when the coefficient matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform $N-x$ contingency analysis, i.e., determine the state of the system when up to $x$ links from $N$ fail. Our algorithms augment the coefficient matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms, a direct method, and a hybrid direct-iterative method for solving the augmented system. We also exploit the sparsity of the matrices and vectors to accelerate the overall computation. Our algorithms are compared on three power grids with PARDISO, a parallel direct solver, and CHOLMOD, a direct solver with the ability to modify the Cholesky factors of the coefficient matrix. We show that our augmented algorithms outperform PARDISO (by two orders of magnitude), and CHOLMOD (by a factor of up to 5). Further, our algorithms scale better than CHOLMOD as the number of elements updated increases. The solutions are computed with high accuracy. Our algorithms are capable of computing $N-x$ contingency analysis on a $778K$ bus grid, updating a solution with $x=20$ elements in $1.6 \times 10^{-2}$ seconds on an Intel Xeon processor.

Yeung, Yu-Hong↗

DOE OSTI2016

Dragonfly : an implementation of the expand–maximize–compress algorithm for single-particle imaging

Single-particle imaging (SPI) with X-ray free-electron lasers has the potential to change fundamentally how biomacromolecules are imaged. The structure would be derived from millions of diffraction patterns, each from a different copy of the macromolecule before it is torn apart by radiation damage. The challenges posed by the resultant data stream are staggering: millions of incomplete, noisy and un-oriented patterns have to be computationally assembled into a three-dimensional intensity map and then phase reconstructed. In this paper, the Dragonfly software package is described, based on a parallel implementation of the expand–maximize–compress reconstruction algorithm that is well suited for this task. Auxiliary modules to simulate SPI data streams are also included to assess the feasibility of proposed SPI experiments at the Linac Coherent Light Source, Stanford, California, USA.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Toward active disruption avoidance via real-time estimation of the safe operating region and disruption proximity in tokamaks

This paper describes a real-time capable algorithm for identifying the safe operating region around a tokamak operating point. The region is defined by a convex set of linear constraints, from which the distance of a point from a disruptive boundary can be calculated. The disruptivity of points is calculated from an empirical machine learning predictor that generates the likelihood of disruption. While the likelihood generated by such empirical models can be compared to a threshold to trigger a disruption mitigation system, the safe operating region calculation enables active optimization of the operating point to maintain a safe margin from disruptive boundaries. The proposed algorithm is tested using a random forest disruption predictor fit on data from DIII-D. The safe operating region identification algorithm is applied to historical data from DIII-D showing the evolution of disruptive boundaries and the potential impact of optimization of the operating point. Real-time relevant execution times are made possible by parallelizing many of the calculation steps and implementing the algorithm on a graphics processing unit. Lastly, a real-time capable algorithm for optimizing the target operating point within the identified constraints is also proposed and simulated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Petascale Application of a Coupled CPU-GPU Algorithm for Simulation and Analysis of Multiphase Flow Solutions in Porous Medium Systems, In: 2014 IEEE 28th International Parallel and Distributed Processing Symposium

Large-scale simulation can provide a wide range of information needed to develop and validate theoretical models for multiphase flow in porous medium systems. In this paper, we consider a coupled solution in which a multiphase flow simulator is coupled to an analysis approach used to extract the interfacial geometries as the flow evolves. This has been implemented using MPI to target heterogeneous nodes equipped with GPUs. The GPUs evolve the multiphase flow solution using the lattice Boltzmann method while the CPUs compute up scaled measures of the morphology and topology of the phase distributions and their rate of evolution. Our approach is demonstrated to scale to 4,096 GPUs and 65,536 CPU cores to achieve a maximum performance of 244,754 million-lattice-node updates per second (MLUPS) in double precision execution on Titan. In turn, this approach increases the size of systems that can be considered by an order of magnitude compared with previous work and enables detailed in situ tracking of averaged flow quantities at temporal resolutions that were previously impossible. Furthermore, it virtually eliminates the need for post-processing and intensive I/O and mitigates the potential loss of data associated with node failures.

Computer Science↗

DOE OSTI2013

Massive hybrid parallelism for fully implicit multiphysics

As hardware advances continue to modify the supercomputing landscape, traditional scientific software development practices will become more outdated, ineffective, and inefficient. The process of rewriting/retooling existing software for new architectures is a Sisyphean task, and results in substantial hours of development time, effort, and money. Software libraries which provide an abstraction of the resources provided by such architectures are therefore essential if the computational engineering and science communities are to continue to flourish in this modern computing environment. The Multiphysics Object Oriented Simulation Environment (MOOSE) framework enables complex multiphysics analysis tools to be built rapidly by scientists, engineers, and domain specialists, while also allowing them to both take advantage of current HPC architectures, and efficiently prepare for future supercomputer designs. MOOSE employs a hybrid shared-memory and distributed-memory parallel model and provides a complete and consistent interface for creating multiphysics analysis tools. In this paper, a brief discussion of the mathematical algorithms underlying the framework and the internal object-oriented hybrid parallel design are given. Representative massively parallel results from several applications areas are presented, and a brief discussion of future areas of research for the framework are provided. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Scalable, In-situ Data Clustering Data Analysis for Extreme Scale Scientific Computing (Final Report)

The objective of this project is to address challenges in the design and development of scalable in-situ data clustering and analytics algorithms and software. Our goal is to develop parallel software consisting of a set of spatio-temporal data clustering and anomaly detection functions, both of which are very important for large-scale analysis and have wide applicability for in-situ runs as well as post-processing analysis. Our design principles for in-situ analysis consider the following: (1) identify parts of the computation can be done close to the data within the nodes, while it is still in memory; (2) extract analysis components can (and should) be performed in remote staging and analysis nodes; (3) develop error-bound approximation methods for applications tolerable for small errors; (4) identify the type of derived distributions and statistics, for spatio-temporal data, that can be kept locally in order to both accelerate computations and meet energy constraints in subsequent iterations and phases; (5) use a self-describing data format so that data can be consistent and understood among local storage (memory and SSDs) and at staging and analysis nodes, thereby providing portability and flexibility; (6) develop service-oriented functions that can schedule in-situ and post-hoc analysis tasks based on the dynamic requirements of applications. Our development focus is to produce the parallel data analysis software/library that will be scalable, reusable, extensible, and generic for applications in different disciplines. The software will be able to run in-situ with the simulations as well as post-hoc analysis. This approach will satisfy many synergistic requirements for data intensive applications executed on data coming from instruments and experiments. In particular, the proposed multilevel approach is directly applicable to perform design tradeoffs for running part of the algorithms near the instruments and the rest on remote (analysis) systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Spatiotemporal parallelization of an analytical heat conduction model for additive manufacturing via a hybrid OpenMP + MPI approach

The ability to do thermal simulations for entire additive manufacturing builds is a key computational problem facing the additive manufacturing community; however, complex numerical models considering multiple physical phenomena currently do not have the capacity for simulations at this scale. To this end, conduction only analytic models offer a viable approach due to the massive drop in computational expense. In this work, we extend an existing implementation which uses a governing equation which can be evaluated at any point in space and time. This implementation already utilizes OpenMP with a spatial decompositions scheme stemming from a melt pool tracking algorithm. Furthermore, we then combine this with a parallel in time (PinT) approach to make the problem highly parallelizable. The new scheme, which uses MPI for internode communication and OpenMP for intranode communication, is shown to scale very well across multiple computational nodes. This approach results in the ability to simulate the 3D solidification conditions for entire layers of additively manufactured parts in minutes making part scale thermal simulations more practical.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Accelerating Lattice QCD Multigrid on GPUs Using Fine-Grained Parallelization

The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using multi-grid algorithms, and due to the throughput improvements brought by GPUs. Deploying hierarchical algorithms optimally on GPUs is non-trivial owing to the lack of parallelism on the coarse grids, and as such, these advances have not proved multiplicative. Using the QUDA library, we demonstrate that by exposing all sources of parallelism that the underlying stencil problem possesses, and through appropriate mapping of this parallelism to the GPU architecture, we can achieve high efficiency even for the coarsest of grids. Results are presented for the Wilson-Clover discretization, where we demonstrate up to 10x speedup over present state-of-the-art GPU-accelerated methods on Titan. Finally, we look to the future, and consider the software implications of our findings.

Clark, M. A.↗

DOE OSTI2016

Characterization of bandwidth requirements of algorithms for extreme scale science

Technology trends have resulted in widely different rates of improvement in computational throughput as compared to data movement rates in computer systems. With future systems, the cost of data movement through the memory hierarchy is expected to become even more dominant relative to the cost of performing arithmetic operations, both in terms of time and energy. Therefore, optimizing data access costs will become ever more critical in the coming years. However, unlike the well understood model of computational complexity in terms of the number of elementary operations to execute an algorithm, the inherent data-movement complexity of computations is unknown for most algorithms. Given the crucial importance of optimizing data access costs in scalable parallel systems, it is of great interest to develop techniques for understanding the inherent data movement complexity of an algorithm. In this project, we focus on this fundamental and significant problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

On the Degradation of the Effectiveness of Nonlinear Diffusion Acceleration with Parallel Block Jacobi Splitting

MOOSE's radiation transport module Rattlesnake comprises a first order S N solver that can be accelerated with a flexible Nonlinear Diffusion Acceleration. At each NDA iteration, the streaming and collision operator of the S{sub N} equations are (approximately) inverted using a transport sweep. When executed on multiple processors parallel block Jacobi (PBJ) splitting is utilized lagging the processor sub-domain's incoming angular fluxes making the implemented method asynchronous, i.e. the convergence properties of NDA become dependent on the number of concurrent tasks and details of the partitioning. Within this work, we study the NDA convergence properties for the two-dimensional C5G7 benchmark problem PBJ with p = 1, 2, 4, 8, 12, 16, 24, 32, 48, 60, 72, 96 and 144 concurrent tasks. Rosa studied the convergence properties of PBJ splitting methods with and without transport synthetic acceleration (TSA) in slab geometry and two-dimensional Cartesian geometry, respectively. Rosa's iteration scheme lags both the incoming angular fluxes and the scattering source making it very similar to the method described here. Rosa found by means of Fourier analysis that convergence of unaccelerated PBJ can degrade for optically thin subdomains, i.e. for a large number of processors given a fixed domain size. Depending on the choice of parameters application of TSA can lead to an effective algorithm. In contrast to Rosa's work, this work focuses on PBJ splitting for NDA accelerated solution of the multigroup eigenvalue problem. Later, Zerr and Anistratov used their integral transport matrix method in conjunction with PBJ. This iteration scheme is different as it does not lag the scattering source. Nevertheless, Fourier analysis with Diamond Difference spatial discretization showed that the method degrades with increasing the overall size of the spatial domain while keeping the sub-domain size constant. In the case of an infinite medium, the observed spectral radius becomes unity. These references establish the iterative performance of PBJ for one-group fixed source problems discretized on rectangular cells, but for the Rattlesnake first order NDA method, an emphasis lies on multigroup eigenvalue problems. In this setting, the additional complication arises that the low order equations are not exactly inverted, but only to some iterative criterion. Further, as the low order problem is solved using Jacobian-Free Newton Krylov methods, a suitable preconditioner for the GMRES iterations is required. As the effectiveness of the preconditioners may decrease when more concurrent processes are used, we expect the low order solve to impact the overall effectiveness of the NDA method in parallel execution as well. Therefore, this work focuses on the question of how detrimental the asynchronicity of the high and low order iterative solutions is for the effectiveness of NDA solutions of realistic, unstructured grid, multigroup eigenvalue problems. The iterative convergence properties of Rattlesnake's NDA method for multigroup eigenvalue problems are studied for varying number of concurrent processes. Rattlesnake's NDA method is asynchronous because the high order transport sweep uses PBJ splitting and because the low order solve's preconditioners, algebraic multigrid and additive Schwarz, are asynchronous. We found that up to 144 processes the number of Picard iterations increases by a factor of 2-3 affecting but not destroying NDA's parallel performance for the C5G7 benchmark problem, a representative LWR (light water reactor) configuration. The solution of the NDA low order eigenvalue problem posed greater problems than expected for the solvers currently available in Rattlesnake mainly because of problems to effectively precondition the modified low-order problem. As a matter of fact, the low order problem becomes an advection-diffusion problem. Non-robustness was observed for the AMG preconditioned coarse mesh acceleration for more than 60 concurrent processes, which was fixed by increasing the number of permissible V-cycles per AMG call. For fine mesh acceleration AMG proved to be ineffective and we resorted to ASM. For both AMG and ASM, increasing number of linear iterations per nonlinear are observed when increasing the number of processes, but for ASM this problem appears to be worse. The results from this work also indicate that initial development efforts should be diverted from implementation of a high-order parallel sweeping algorithm to the effective and robust iterative solution of the low order NDA multigroup eigenvalue problem. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Distributed Reinforcement Learning with ADMM-RL

This paper presents a new algorithm for distributed Reinforcement Learning (RL). RL is an artificial intelligence (AI) control strategy such that controls for highly nonlinear systems over multi-step time horizons may be learned by experience, rather than directly computed on the fly by optimization. Here we introduce ADMM-RL, a combination of the Alternating Direction Method of Multipliers (ADMM) and reinforcement learning that allows for integrating learned controllers as subsystems in generally convergent distributed control applications. ADMM has become the workhorse algorithm for distributed control, combining the advantages of dual decomposition (namely, enabling decoupled, parallel, distributed solution) with the advantages of the method of multipliers (namely, convexification/stability). Our ADMM-RL algorithm replaces one or more of the subproblems in ADMM with several steps of RL. When the nested iterations converge, we are left with a pretrained subsolver that can potentially increase the efficiency of the deployed distributed controller by orders of magnitude. We illustrate ADMM-RL in both distributed wind farm yaw control and distributed grid-aware demand aggregation for water heaters.

ADMM↗

DOE OSTI2025

Toucan: A performance portable, scalable implementation of the DECA algorithm

In the field of additive manufacturing (AM), cellular automata (CA) is extensively used to simulate microstructural evolution during solidification. However, while traditional CA approaches are relatively fast, they still require a substantial number of time steps, are limited to moderate volumes, and are relatively difficult to improve through parallelism due to the highly localized nature of the solidification front. Here, to address these issues of time to solution and load balancing, we introduce Toucan, a parallel, performance-portable, and scalable code written in C++ with the Kokkos library that leverages the discrete event inspired cellular automata (DECA) algorithm to perform parallel-in-time (PinT) grain growth simulations. Toucan effectively mitigates load balancing issues by distributing the computational workload more evenly across processors, enhancing scalability and efficiency. We conduct both strong and weak scaling studies on up to 64 GPUs on the Frontier supercomputer, demonstrating that Toucan significantly outperforms the current state-of-the-art, time-stepped CA code, ExaCA, on both single and multi-GPU simulations. Even in AM-specific weak scaling scenarios, Toucan maintains near-ideal scaling, in contrast to the linear increase observed with ExaCA due to the moving laser raster pattern. This study highlights Toucan’s potential to transform microstructural simulations in AM by radically improving both efficiency and scalability over existing methods.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Preliminary performance evaluation of P++ single event proton scattering algorithms on GPUS - 25688

A need has been realized for fast, accurate charged particle transport in a wide variety of domains. Utilizing hardware acceleration through GPUs now common in user desktops, speedups in simulation comparable to those found with HPC systems can be realized for a fraction of the price. Preliminary results on the P++ proton transport code developed by the Rensselaer Radiation Measurement and Dosimetry Group (RRMDG) are presented. The code has been validated for the 1 GeV to 1 MeV energy regime and is targeted to benefit application areas such as proton radiography, space radiation research, and clinical accelerator therapy. The code is notable for employing a single event, 'on the fly' cross section based transport algorithm rather than the traditional condensed history or step based method seen in many production Monte Carlo codes. Performance improvements for the P++ code have been introduced through MPI parallelization as well as a CUDA version of the transport algorithm capable of running on NVidia GPUs. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2013

MASSIVE HYBRID PARALLELISM FOR FULLY IMPLICIT MULTIPHYSICS

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Direction-optimizing Label Propagation Framework for Structure Detection in Graphs: Design, Implementation, and Experimental Analysis

Label Propagation is not only a well-known machine learning algorithm for classification but also an effective method for discovering communities and connected components in networks. We propose a new Direction-optimizing Label Propagation Algorithm (DOLPA) framework that enhances the performance of the standard Label Propagation Algorithm (LPA), increases its scalability, and extends its versatility and application scope. As a central feature, the DOLPA framework relies on the use of frontiers and alternates between label push and label pull operations to attain high performance. It is formulated in such a way that the same basic algorithm can be used for finding communities or connected components in graphs by only changing the objective function used. Additionally, DOLPA has parameters for tuning the processing order of vertices in a graph to reduce the number of edges visited and improve the quality of solution obtained. We present the design and implementation of the enhanced algorithm as well as our shared-memory parallelization of it using OpenMP. We also present an extensive experimental evaluation of our implementations using the LFR benchmark and real-world networks drawn from various domains. Compared with an implementation of LPA for community detection available in a widely used network analysis software, we achieve at most five times the F-Score while maintaining similar runtime for graphs with overlapping communities. We also compare DOLPA against an implementation of the Louvain method for community detection using the same LFR-graphs and show that DOLPA achieves about three times the F-Score at just 10% of the runtime. For connected component decomposition, our algorithm achieves orders of magnitude speedups over the basic LP-based algorithm on large-diameter graphs, up to 13.2× speedup over the Shiloach-Vishkin algorithm, and up to 1.6× speedup over Afforest on an Intel Xeon processor using 40 threads.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Parallel auto-correlative statistics with VTK.

This report summarizes existing statistical engines in VTK and presents both the serial and parallel auto-correlative statistics engines. It is a sequel to [PT08, BPRT09b, PT09, BPT09, PT10] which studied the parallel descriptive, correlative, multi-correlative, principal component analysis, contingency, k-means, and order statistics engines. The ease of use of the new parallel auto-correlative statistics engine is illustrated by the means of C++ code snippets and algorithm verification is provided. This report justifies the design of the statistics engines with parallel scalability in mind, and provides scalability and speed-up analysis results for the autocorrelative statistics engine.

Pebay, Philippe Pierre↗

DOE OSTI2016

Numerical methods for high-dimensional probability density function equations

In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗