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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

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.

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↗

DOE OSTI2024

Active Learning for Metamaterial Optimization on HPC and QC Integrated Systems

Active learning algorithms, integrating machine learning, quantum computing and optics simulation in an iterative loop, offer a promising approach to optimizing metamaterials. However, these algorithms can face difficulties in optimizing highly complex structures due to computational limitations. High-performance computing (HPC) and quantum computing (QC) integrated systems can address these issues by enabling parallel computing. In this study, we develop an active learning algorithm working on HPC-QC integrated systems. We evaluate the performance of optimization processes within active learning (i.e., training a machine learning model, problem-solving with quantum computing, and evaluating optical properties through wave-optics simulation) for highly complex metamaterial cases. Our results showcase that utilizing multiple cores on the integrated system can significantly reduce computational time, thereby enhancing the efficiency of optimization processes. Therefore, we expect that leveraging HPC-QC integrated systems helps effectively tackle large-scale optimization challenges in general.

Kim, Seongmin↗

DOE OSTI2012

File I/O for MPI Applications in Redundant Execution Scenarios

As multi-petascale and exa-scale high-performance computing (HPC) systems inevitably have to deal with a number of resilience challenges, such as a significant growth in component count and smaller circuit sizes with lower circuit voltages, redundancy may offer an acceptable level of resilience that traditional fault tolerance techniques, such as checkpoint/restart, do not. Although redundancy in HPC is quite controversial due to the associated cost for redundant components, the constantly increasing number of cores-per-processor is tilting this cost calculation toward a system design where computation, such as for redundancy, is much cheaper and communication, needed for checkpoint/restart, is much more expensive. Recent research and development activities in redundancy for Message Passing Interface (MPI) applications focused on availability/reliability models and replication algorithms. This paper takes a first step toward solving an open research problem associated with running a parallel application redundantly, which is file I/O under redundancy. The approach intercepts file I/O calls made by a redundant application to employ coordination protocols that execute file I/O operations in a redundancy-oblivious fashion when accessing a node-local file system, or in a redundancy-aware fashion when accessing a shared networked file system. A proof-of concept prototype is presented and a number of coordination protocols are described and evaluated. The results show the performance impact for redundantly accessing a shared networked file system, but also demonstrate the capability to regain performance by utilizing MPI communication between replicas and parallel file I/O.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

Causal explicit algorithm for heat conduction in a plasma

Hyperbolic heat conduction extends standard Spitzer-Harm heat conduction by including a term proportional to the time derivative of the heat flux. The new term arises from a kinetic derivation of the heat flux that includes higher order corrections. Here we present a causal explicit numerical algorithm for solving the nonlinear hyperbolic heat conduction equation in an unmagnetized plasma. The maximum stable timestep for the causal explicit algorithm scales linearly with the cell size, owing to the hyperbolic nature of the problem. This is in contrast to the quadratic scaling of the maximum stable timestep with the cell size for the parabolic forward time centered space algorithm. The favorable scaling of the timestep with the cell size enables a practical explicit implementation of heat conduction in high-performance massively parallel plasma codes. In particular, we have implemented the causal explicit algorithm in the laser plasma interaction code pF3D. We verify the CE algorithm and analyze its convergence rate by simulating a harmonic mode, which has an analytic solution within the context of the HHC model. We also compare simulations using the CE algorithm to those using the forward time centered space algorithm on a pair of test problems: evolution in time of a Gaussian temperature perturbation in a uniform plasma and heat transport in the presence of inverse bremsstrahlung heating by a Gaussian laser speckle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Distributed merge trees

Improved simulations and sensors are producing datasets whose increasing complexity exhausts our ability to visualize and comprehend them directly. To cope with this problem, we can detect and extract significant features in the data and use them as the basis for subsequent analysis. Topological methods are valuable in this context because they provide robust and general feature definitions. As the growth of serial computational power has stalled, data analysis is becoming increasingly dependent on massively parallel machines. To satisfy the computational demand created by complex datasets, algorithms need to effectively utilize these computer architectures. The main strength of topological methods, their emphasis on global information, turns into an obstacle during parallelization. We present two approaches to alleviate this problem. We develop a distributed representation of the merge tree that avoids computing the global tree on a single processor and lets us parallelize subsequent queries. To account for the increasing number of cores per processor, we develop a new data structure that lets us take advantage of multiple shared-memory cores to parallelize the work on a single node. Finally, we present experiments that illustrate the strengths of our approach as well as help identify future challenges. Copyright © 2013 ACM 978-1-4503-1922-5/13/ 02...$15.00.

Morozov, D↗

DOE OSTI2013

Distributed Merge Trees

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Theoretical Plasma Physics

Lattice Boltzmann algorithms are a mesoscopic method to solve problems in nonlinear physics which are highly parallelized – unlike the direction solution of the original problem. These methods are applied to both fluid and magnetohydrodynamic turbulence. By introducing entropic constraints one can enforce the positive definiteness of the distribution functions and so be able to simulate fluids at high Reynolds numbers without numerical instabilities. By introducing a vector distribution function for the magnetic field one can enforce the divergence free condition on the magnetic field automatically, without the need of divergence cleaning as needed in most direct numerical solutions of the resistive magnetohydrodynamic equations. The principal reason for the high parallelization of lattice Boltzmann codes is that they consist of a kinetic collisional relaxation step (which is purely local) followed by a simple shift of the relaxed data to neighboring lattice sites. In large eddy simulations, the closure schemes are highly nonlocal – the most famous of these schemes is that due to Smagorinsky. Under a lattice Boltzmann representation the Smagorinsky closure is purely local – being simply a particular moment on the perturbed distribution fucntions. After nonlocal fluid moment models were discovered to represent Landau damping, it was found possible to model these fluid models using an appropriate lattice Boltzmann algorithm. The close to ideal parallelization of the lattice Boltzmann codes permitted us to be Gordon Bell finalists on using the Earth Simulation in Japan. We have also been involved in the radio frequency propagation of waves into a tokamak and into a spherical overdense tokamak plasma. Initially we investigated the use of a quasi-optical grill for the launching of lower hybrid waves into a tokamak. It was found that the conducting walls do not prevent the rods from being properly irradiated, the overloading of the quasi-optical grill is not severe with the electric field only being about three times higher than in the ideal case. Moreover, the quasi-optical grill was significantly fewer structural elements that the multijunction grill. Nevertheless there has not been much interest from experimental fusion groups to implementing these structures. Hence we have returned to optimizing the multijunction grill so that the large number of coupling matrix elements can be efficiently evaluated using symmetry arguments. In overdense plasmas, the standard electromagnetic waves cannot propagate into the plasma center, but are reflected at the plasma edge. By optimizing mode conversion processes (in particular, the O-X-B wave propagation of Ordinary Mode converting to an Extraordinary mode which then converts into an electrostatic Bernstein wave) one can excite within the plasma an electrostatic Bernstein wave that does not suffer density cutoffs and is absorbed on the electron cyclotron harmonics. Finally we have started looking at other mesoscopic lattice algorithms that involve unitary collision and streaming steps. Because these algorithms are unitary they can be run on quantum computers when they become available – unlike their computational cousin of lattice Boltzmann which is a purely classical code. These quantum lattice gas algorithms have been tested successfully on exact analytic soliton collision solution. These calculations are hoped to be able to study Bose Einstein condensed atomic gases and their ground states in an optical lattice.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗