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DOE OSTI2022

A Non-perturbative Approach to Computing Seismic Normal Modes in Rotating Planets

In this work, a continuous Galerkin method based approach is presented to compute the seismic normal modes of rotating planets. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core using a polynomial filtering eigensolver. The relevant elastic-gravitational system of equations, including the Coriolis force, is subjected to a mixed finite-element method, while self-gravitation is accounted for with the fast multipole method. Our discretization utilizes fully unstructured tetrahedral meshes for both solid and fluid regions. The relevant eigenvalue problem is solved by a combination of several highly parallel and computationally efficient methods. We validate our three-dimensional results in the non-rotating case using analytical results for constant elastic balls, as well as numerical results for an isotropic Earth model from standard “radial” algorithms. We also validate the computations in the rotating case, but only in the slowly-rotating regime where perturbation theory applies, because no other independent algorithms are available in the general case. The algorithm and code are used to compute the point spectra of eigenfrequencies in several Earth and Mars models studying the effects of heterogeneity on a large range of scales.

58 GEOSCIENCES↗

DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Effective Ion Mobility Calculations for Macromolecules by Scattering off Electron Clouds

Broad commercialization and increasing resolving power of ion mobility spectrometry/mass spectrometry (IMS/MS) platforms has engendered an explosion of IMS applications to structural characterization of gas-phase biomolecules. That has renewed interest in more accurate and rapid ion mobility calculations needed to elicit ion geometries from the measurements. An approach based on scattering off electron density isosurfaces (SEDI) that mirrors the physics of molecular collisions was proven superior to the common methods involving atomic coordinates a decade ago, but has remained impractical for large ions because of extreme computational demands. Here, we accelerate SEDI by up to ~500 times using the fragment molecular orbital (FMO) approach for surface generation and the multiplexed scattering algorithm in conjunction with the new grid extrapolation procedure for cross section evaluations. Parallelization of the code on a supercomputer has produced major further speed gains, allowing SEDI calculations for proteins (defined by over a million surface points) with the precision of <0.1% in one minute. Initial tests reveal the anticipated dependences of mobility on the ion charge state and lower cross sections in view of reduced surface roughness. Present developments are expected to lead to broad application of SEDI in IMS studies of macromolecules, enabling more accurate and reliable structural assignments.

Alexeev, Yuri↗

DOE OSTI2012

Hybrid algorithms in quantum Monte Carlo

With advances in algorithms and growing computing powers, quantum Monte Carlo (QMC) methods have become a leading contender for high accuracy calculations for the electronic structure of realistic systems. The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the number of SMPs have been going up, as the Top500 list attests. However, the available memory as well as the communication and memory bandwidth per element has not kept pace with the increasing parallelism. This severely limits the applicability of QMC and the problem size it can handle. OpenMP/MPI hybrid programming provides applications with simple but effective solutions to overcome efficiency and scalability bottlenecks on large-scale clusters based on multi/many-core SMPs. We discuss the design and implementation of hybrid methods in QMCPACK and analyze its performance on current HPC platforms characterized by various memory and communication hierarchies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Automated Calibration of Parallel and Distributed Computing Simulators: A Case Study

Many parallel and distributed computing research results are obtained in simulation, using simulators that mimic real-world executions on some target system. Each such simulator is configured by picking values for parameters that define the behavior of the underlying simulation models it implements. The main concern for a simulator is accuracy: simulated behaviors should be as close as possible to those observed in the real-world target system. This requires that values for each of the simulator's parameters be carefully picked, or “calibrated,” based on ground-truth real-world executions. Examining the current state of the art shows that simulator calibration, at least in the field of parallel and distributed computing, is often undocumented (and thus perhaps often not performed) and, when documented, is described as a labor-intensive, manual process. In this work we evaluate the benefit of automating simulation calibration using simple algorithms. Specifically, we use a real-world case study from the field of High Energy Physics and compare automated calibration to calibration performed by a domain scientist. Our main finding is that automated calibration is on par with or significantly outperforms the calibration performed by the domain scientist. Furthermore, automated calibration makes it straightforward to operate desirable tradeoffs between simulation accuracy and simulation speed.

Mc donald, Jesse↗

DOE OSTI2014

Scalable Nonlinear Compact Schemes

In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

CSRI Summer Proceedings 2021

The Computer Science Research Institute (CSRI) brings university faculty and students to Sandia National Laboratories for focused collaborative research on Department of Energy (DOE) computer and computational science problems. The institute provides an opportunity for university researches to learn about problems in computer and computational science at DOE laboratories, and help transfer results of their research to programs at the labs. Some specific CSRI research interest areas are: scalable solvers, optimization, algebraic preconditioners, graph-based, discrete, and combinatorial algorithms, uncertainty estimation, validation and verification methods, mesh generation, dynamic load-balancing, virus and other malicious-code defense, visualization, scalable cluster computers, beyond Moore’s Law computing, exascale computing tools and application design, reduced order and multiscale modeling, parallel input/output, and theoretical computer science. The CSRI Summer Program is organized by CSRI and includes a weekly seminar series and the publication of a summer proceedings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

CSRI Summer Proceedings 2021

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Accelerating DCA++ (Dynamical Cluster Approximation) Scientific Application on the Summit supercomputer

Optimizing scientific applications on today’s accelerator-based high performance computing systems can be challenging, especially when multiple GPUs and CPUs with heterogeneous memories and persistent non-volatile memories are present. An example is Summit, an accelerator-based system at the Oak Ridge Leadership Computing Facility (OLCF) that is rated as the world’s fastest supercomputer to-date. New strategies are thus needed to expose the parallelism in legacy applications, while being amenable to efficient mapping to the underlying architecture.In this paper we discuss our experiences and strategies to port a scientific application, DCA++, to Summit. DCA++ is a highperformance research application that solves quantum manybody problems with a cutting edge quantum cluster algorithm, the dynamical cluster approximation.Our strategies aim to synergize the strengths of the different programming models in the code. These include: (a) streamlining the interactions between the CPU threads and the GPUs, (b) implementing computing kernels on the GPUs and decreasing CPU-GPU memory transfers, (c) allowing asynchronous GPU communications, and (d) increasing compute intensity by combining linear algebraic operations.Full-scale production runs using all 4600 Summit nodes attained a peak performance of 73.5 PFLOPS with a mixed precision implementation.We observed a perfect strong and weak scaling for the quantum Monte Carlo solver in DCA++, while encountering about 2× input/output (I/O) and MPI communication overhead on the time-to-solution for the full machine run. Our hardware agnostic optimizations are designed to alleviate the communication and I/O challenges observed, while improving the compute intensity and obtaining optimal performance on a complex, hybrid architecture like Summit.

Balduzzi, Giovanni↗

DOE OSTI2022

Cabana: A Performance Portable Library for Particle-Based Simulations

Particle-based simulations are ubiquitous throughout many fields of computational science and engineering, spanning the atomistic level with molecular dynamics (MD), to mesoscale particle-in-cell (PIC) simulations for solid mechanics, device-scale modeling with PIC methods for plasma physics, and massive N-body cosmology simulations of galaxy structures, with many other methods in between (Hockney & Eastwood, 1989). While these methods use particles to represent significantly different entities with completely different physical models, many low-level details are shared including performant algorithms for short- and/or long-range particle interactions, multi-node particle communication patterns, and other data management tasks such as particle sorting and neighbor list construction. Cabana is a performance portable library for particle-based simulations, developed as part of the Co-Design Center for Particle Applications (CoPA) within the Exascale Computing Project (ECP) (Alexander et al., 2020). The CoPA project and its full development scope, including ECP partner applications, algorithm development, and similar software libraries for quantum MD, is described in (Mniszewski et al., 2021). Cabana uses the Kokkos library for on-node parallelism (Edwards et al., 2014; Trott et al., 2022), enabling simulation on multi-core CPU and GPU architectures, and MPI for GPU-aware, multi-node communication. Cabana provides particle simulation capabilities on almost all current Kokkos backends, including serial execution, OpenMP (including OpenMP-Target for GPUs), CUDA (NVIDIA GPUs), HIP (AMD GPUs), and SYCL (Intel GPUs), providing a clear path for the coming generation of accelerator-based exascale hardware. Cabana builds on Kokkos by providing new particle data structures and particle algorithms resulting in a similar execution policy-based, node-level programming model that is intended to be used in addition to the core Kokkos library within an application. Cabana is designed as an application and physics agnostic, but particle-specific toolkit which can either be used to generate a new application, or to be used as needed in existing applications at various levels of invasiveness including through interfaces that wrap user memory in existing data structures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Sensitivity Analysis of Passive Heat Removal Capability of FHR Based on Efficient Surrogate Model and GenFlow

Code Scaling, Applicability and Uncertainty Evaluation Methodology (CSAU) is used for quantifying reactor safety margins and works as an alternative method for licensing nuclear power plant. In the framework of CSAU, sensitivity and uncertainty analysis (SA and UA) should be performed. However, for large-scale complicated thermal hydraulics analysis simulated by code (e.g. RELAP5, CFD and subchannel analysis, the sensitivity and uncertainty analysis is really time-consuming. Furthermore, sometimes it is not feasible to perform SA and UA. Specifically, the computation time for Monte Carlo sampling or advanced LHS sampling can be neglected, but the computation time for thermal hydraulics code makes up main part of time during SA and UA process. In order to accelerate the speed of SA and UA, thermal hydraulics code can be improved based on advanced mathematic algorithm or using parallel method. However, the development for new mathematic method needs long time and strict verification and validation process is needed for a new code, which usually takes a couple of years or even longer time to have an approved code that can be used in nuclear industry. An alternative way to improve the speed of SA and UA is using surrogate model. The surrogate model is derived from the input as well as output data of the original code, assuming the code as a black box. The most common method is using response surface method (RSM) as a surrogate for the code, the input parameters are then sampled from their assumed distribution and the corresponding value of the response surface function is calculated. However, a couple of input parameters need hundreds or even thousands of original code calculations. The large number of runs is an obvious disadvantage of this method. Besides, the second disadvantage is an appropriate response surface function must be selected (e.g. quadratic, cubic, quartic, with or without cross product terms, or using a non-polynomial form) to avoid the overfit and underfit problem. This process is time consuming and expensive. Polynomial chaos expansion method is a reasonably fast and attractive alternative, stochastic model. The chaos expansion provides an efficient high-order method of including non-linear effects in stochastic analysis. Usually, the information about the model parameters and their probability distribution is limited and the dependence between them is not known. However, if arbitrary polynomial chaos is used, instead of assuming probability distribution for input parameters which may introduces additional subjectivity into the analysis, the available information can directly and most purely be used in stochastic analysis based on arbitrary data distribution. Thus, it is not necessary to know the exact probability density functions to perform SA and UA based on arbitrary polynomial chaos (aPC). The aPC has been applied for uncertainty quantification in many fields (e.g. in solid mechanics, fluid flows, thermal sciences), and become widely used in nuclear industry recently. Mk1 PB-FHR is a small modular fluoride-salt-cooled, high-temperature reactors (FHRs) that is a concept design by University of California, Berkeley (UCB). It has inherently safe features like natural-circulation-driven systems (e.g. direct reactor auxiliary cooling system (DRACS)) to passively remove decay heat from the reactor core during design basis and beyond design. It is necessary to perform SA and UA, since the licensing process of this new kind of reactor is under way and there are many design parameters that have not been fixed. Current nuclear commercial codes, such as RELAP5, have mainly been developed for light water reactors, which require the use of comprehensive two-phase flow models. This capability is not required to simulate single-phase flow phenomena in FHRs, whose baseline coolant, flibe, remains liquid up to 1430 deg. C at atmospheric pressure. The FHR advanced natural circulation analysis (FANCY) code has been developed specifically for FHR technology modeling and validation work has been performed by using CIET data in UCB. The code has been renamed General Flow (GenFlow) because it has been further developed to have the capability to model complicated pipework system based on object-oriented concept for user friendly purpose. Besides, it can be used to simulate both the force circulation as well as natural circulation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2018

Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry

We present a parallel multi-implicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with complex chemistry. Here, our strategy employs parallelisation across the method to accelerate the serial Multi-Implicit Spectral Deferred Correction (MISDC) scheme used to couple the advection, diffusion, and reaction processes. In our approach, the diffusion solves and the reaction solves are performed concurrently by different processors. Our analysis shows that the proposed parallel scheme is stable for stiff problems and that the sweeps converge to the fixed-point solution at a faster rate than with serial MISDC. We present numerical examples to demonstrate that the new algorithm is high-order accurate in time, and achieves a parallel speedup compared to serial MISDC.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

The VTK-m User's Guide (V. 2.2)

High-performance computing relies on ever finer threading. Advances in processor technology include ever greater numbers of cores, hyperthreading, accelerators with integrated blocks of cores, and special vectorized instructions, all of which require more software parallelism to achieve peak performance. Traditional visualization solutions cannot support this extreme level of concurrency. Extreme scale systems require a new programming model and a fundamental change in how we design algorithms. To address these issues we created VTK-m: the visualization toolkit for multi-/many-core architectures. VTK-m supports a number of algorithms and the ability to design further algorithms through a top-down design with an emphasis on extreme parallelism. VTK-m also provides support for finding and building links across topologies, making it possible to perform operations that determine manifold surfaces, interpolate generated values, and find adjacencies. Although VTK-m provides a simplified high-level interface for programming, its template-based code removes the overhead of abstraction.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Scalability of high-performance PDE solvers

Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Final Report for Award #DE-SC3956 Separating Algorithm and Implementation via programming Model Injection (SAIMI)

Programming parallel machines is fraught with difficulties: the obfuscation of algorithms due to implementation details such as communication and synchronization, the need for transparency between language constructs and performance, the difficulty of performing program analysis to enable automatic parallelization techniques, and the existence of important "dusty deck" codes. The SAIMI project developed abstractions that enable the orthogonal specification of algorithms and implementation details within the context of existing DOE applications. The main idea is to enable the injection of small programming models such as expressions involving transcendental functions, polyhedral iteration spaces with sparse constraints, and task graphs into full programs through the use of pragmas. These smaller, more restricted programming models enable orthogonal specification of many implementation details such as how to map the computation on to parallel processors, how to schedule the computation, and how to allocation storage for the computation. At the same time, these small programming models enable the expression of the most computationally intense and communication heavy portions in many scientific simulations. The ability to orthogonally manipulate the implementation for such computations will significantly ease performance programming efforts and expose transformation possibilities and parameter to automated approaches such as autotuning. At Colorado State University, the SAIMI project was supported through DOE grant DE-SC3956 from April 2010 through August 2015. The SAIMI project has contributed a number of important results to programming abstractions that enable the orthogonal specification of implementation details in scientific codes. This final report summarizes the research that was funded by the SAIMI project.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Pass-efficient methods for compression of high-dimensional turbulent flow data

The future of high-performance computing, specifically on future Exascale computers, will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential equation (PDE) systems. Current strategies proposed to address this bottleneck entail the omission of large fractions of data, as well as the incorporation of in situ compression algorithms to avoid overuse of memory. To ensure that post-processing operations are successful, this must be done in a way that a sufficiently accurate representation of the solution is stored. Moreover, in situations where the input/output system becomes a bottleneck in analysis, visualization, etc., or the execution of the PDE solver is expensive, the number of passes made over the data must be minimized. In the interest of addressing this problem, this work focuses on the utility of pass-efficient, parallelizable, low-rank, matrix decomposition methods in compressing high-dimensional simulation data from turbulent flows. Additionally, a particular emphasis is placed on using coarse representation of the data – compatible with the PDE discretization grid – to accelerate the construction of the low-rank factorization. This includes the presentation of a novel single-pass matrix decomposition algorithm for computing the so-called interpolative decomposition. The methods are described extensively and numerical experiments on two turbulent channel flow data are performed. In the first (unladen) channel flow case, compression factors exceeding 400 are achieved while maintaining accuracy with respect to first- and second-order flow statistics. In the particle-laden case, compression factors of 100 are achieved and the compressed data is used to recover particle velocities. These results show that these compression methods can enable efficient computation of various quantities of interest in both the carrier and disperse phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Optimizing temperature distributions for training neural quantum states using parallel tempering

Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.

Neural network simulations↗

DOE OSTI2019

Scalable Deep Learning via I/O Analysis and Optimization

Scalable deep neural network training has been gaining prominence because of the increasing importance of deep learning in a multitude of scientific and commercial domains. Consequently, a number of researchers have investigated techniques to optimize deep learning systems. Much of the prior work has focused on runtime and algorithmic enhancements to optimize the computation and communication. Despite these enhancements, however, deep learning systems still suffer from scalability limitations, particularly with respect to data I/O. This situation is especially true for training models where the computation can be effectively parallelized, leaving I/O as the major bottleneck. In fact, our analysis shows that I/O can take up to 90% of the total training time. Thus, in this article, we first analyze LMDB, the most widely used I/O subsystem of deep learning frameworks, to understand the causes of this I/O inefficiency. Based on our analysis, we propose LMDBIO—an optimized I/O plugin for scalable deep learning. LMDBIO includes six novel optimizations that together address the various shortcomings in existing I/O for deep learning. Lastly, our experimental results show that LMDBIO significantly outperforms LMDB in all cases and improves overall application performance by up to 65-fold on a 9,216-core system.

97 MATHEMATICS AND COMPUTING↗