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At least 217 records · Page 12

Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory

Direct simulation of the von Neumann dynamics for a general (pure or mixed) quantum state can often be expensive. One prominent example is the real-time time-dependent density functional theory (rt-TDDFT), a widely used framework for the first principle description of many-electron dynamics in chemical and materials systems. Practical rt-TDDFT calculations often avoid the direct simulation of the von Neumann equation, and solve instead a set of Schrödinger equations, of which the dynamics is equivalent to that of the von Neumann equation. However, the time step size employed by the Schrödinger dynamics is often much smaller. Here, in order to improve the time step size and the overall efficiency of the simulation, we generalize a recent work of the parallel transport (PT) dynamics for simulating pure states [An, Lin, Multiscale Model. Simul. 18, 612, 2020] to general quantum states. The PT dynamics provides the optimal gauge choice, and can employ a time step size comparable to that of the von Neumann dynamics. Going beyond the linear and near adiabatic regime in previous studies, we find that the error of the PT dynamics can be bounded by certain commutators between Hamiltonians, density matrices, and their derived quantities. Such a commutator structure is not present in the Schrödinger dynamics. We demonstrate that the parallel transport-implicit midpoint (PT-IM) method is a suitable method for simulating the PT dynamics, especially when the spectral radius of the Hamiltonian is large. The commutator structure of the error bound, and numerical results for model rt-TDDFT calculations in both linear and nonlinear regimes, confirm the advantage of the PT dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Parallel streaming between heterogeneous HPC resources for real-time analysis

Performing analysis or generating visualizations concurrently with high performance simulations can yield great benefits compared to post-processing data. Writing and reading large volumes of data can be reduced or eliminated, thereby producing an I/O cost savings. One such method for concurrent simulation and analysis is in transit - streaming data from the resource running the simulation to a separate resource running the analysis. In transit analysis can be beneficial since computational resources may not have certain resources needed for visualization and analysis (e.g. GPUs) and to reduce the impact of performing analysis tasks to the run time of the simulation. When sending and receiving data in transit, data redistribution mechanisms are needed in order to support heterogeneous data layouts that may be required by the simulation and analysis applications. The work described in this paper compares two mechanisms for on-the-fly data redistribution when streaming data in parallel between two distributed memory applications. Finally, our results show that it is often more advantageous to stream data in the same layout as the sender and redistribute data amongst processes on the receiving end than to stream data in the final layout needed by the receiver.

97 MATHEMATICS AND COMPUTING↗

Parallel variable selection for effective performance prediction

Large data analysis problems often involve a large number of variables, and the corresponding analysis algorithms may examine all variable combinations to find the optimal solution. For example, to model the time required to complete a scientific workflow, we need to consider the impact of dozens of parameters. To reduce the model building time and reduce the likelihood of overfitting, we look to variable selection methods to identify the critical variables for the performance model. In this work, we create a combination of variable selection and performance prediction methods that is as effective as the exhaustive search approach when the exhaustive search could be completed in a reasonable amount of time. To handle the cases where the exhaustive search is too time consuming, we develop the parallelized variable selection algorithm. Additionally, we develop a parallel grouping mechanism that further reduces the variable selection time by 70%.As a case study, we exercise the variable selection technique with the performance measurement data from the Palomar Transient Factory (PTF) workflow. The application scientists have determined that about 50 variables and parameters are important to the performance of the workflows. Our tests show that the Sequential Backward Selection algorithm is able to approximate the optimal subset relatively quickly. By reducing the number of variables used to build the model from 50 to 4, we are able to maintain the prediction quality while reducing the model building time by a factor of 6. Using the parallelization and grouping techniques we developed in this work, the variable selection process was reduced from over 18 hours to 15 minutes while ending up with the same variable subset.

Wang, J↗

Speedup of UEDGE Parameter Scans Using Machine-Learning Optimized OpenMP Parallelization and a Continuation Solver

This article presents the OpenMP parallelization of the preconditioning Jacobian assembly and right‐hand side residual evaluation in UEDGE. A continuation algorithm, utilizing the internal NKSOL implicit Jacobian‐Free Newton‐Krylov solver to efficiently scan physical parameters, is also presented. The implemented parallelization reduces the computational time for a benchmark scan run on 32 threads by compared to the serial version when using trained random forest regression models to identify the optimal decomposition of the system of equations. Random forest regression models applied to the UEDGE time‐dependent and continuation solver algorithms did not yield meaningful improvement in computational performance. A benchmark DIII‐D gas injection rate scan in the 0.35–0.75 kA interval, performed on a test cluster using the parallelized code and continuation solver, produced 1066 steady‐state solutions with a 22 s average wall‐clock computational time per steady‐state solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .

97 MATHEMATICS AND COMPUTING↗

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

36 MATERIALS SCIENCE↗

Layer-Parallel Training of Deep Residual Neural Networks

Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be interpreted as forward Euler discretizations of a nonlinear initial value problem whose time-dependent control variables represent the weights of the neural network. Hence, training a ResNet can be cast as an optimal control problem of the associated dynamical system. For similar time-dependent optimal control problems arising in engineering applications, parallel-in-time methods have shown notable improvements in scalability. This paper demonstrates the use of those techniques for efficient and effective training of ResNets. The proposed algorithms replace the classical (sequential) forward and backward propagation through the network layers with a parallel nonlinear multigrid iteration applied to the layer domain. This adds a new dimension of parallelism across layers that is attractive when training very deep networks. From this basic idea, we derive multiple layer-parallel methods. The most efficient version employs a simultaneous optimization approach where updates to the network parameters are based on inexact gradient information in order to speed up the training process. Finally, using numerical examples from supervised classification, we demonstrate that the new approach achieves a training performance similar to that of traditional methods, but enables layer-parallelism and thus provides speedup over layer-serial methods through greater concurrency.

97 MATHEMATICS AND COMPUTING↗

Cosmic-Ray Diffusion Coefficients throughout the Inner Heliosphere from a Global Solar Wind Simulation

We use a three-dimensional magnetohydrodynamic simulation of the solar wind to calculate cosmic-ray diffusion coefficients throughout the inner heliosphere (2 R{sub ⊙}−3 au). The simulation resolves large-scale solar wind flow, which is coupled to small-scale fluctuations through a turbulence model. Simulation results specify background solar wind fields and turbulence parameters, which are used to compute diffusion coefficients and study their behavior in the inner heliosphere. The parallel mean free path (mfp) is evaluated using quasi-linear theory, while the perpendicular mfp is determined from nonlinear guiding center theory with the random ballistic interpretation. Several runs examine varying turbulent energy and different solar source dipole tilts. We find that for most of the inner heliosphere, the radial mfp is dominated by diffusion parallel to the mean magnetic field; the parallel mfp remains at least an order of magnitude larger than the perpendicular mfp, except in the heliospheric current sheet, where the perpendicular mfp may be a few times larger than the parallel mfp. In the ecliptic region, the perpendicular mfp may influence the radial mfp at heliocentric distances larger than 1.5 au; our estimations of the parallel mfp in the ecliptic region at 1 au agree well with the Palmer “consensus” range of 0.08–0.3 au. Solar activity increases perpendicular diffusion and reduces parallel diffusion. The parallel mfp mostly varies with rigidity (P) as P{sup .33}, and the perpendicular mfp is weakly dependent on P. The mfps are weakly influenced by the choice of long-wavelength power spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty

Practical solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We report computational experiments that demonstrate the ability to solve very large stochastic programming problems - including mixed-integer variants - in minutes of wall clock time, efficiently leveraging significant parallel computing resources. We report results for the largest publicly available instances of stochastic mixed-integer unit commitment problems, solving to provably tight optimality gaps. In addition, we introduce a novel software architecture that facilitates combinations of methods for accelerating convergence that can be combined in plug-and-play manner. Finally, the mpi-sppy package is written in Python, leverages the widely used Pyomo (http://www.pyomo.org) library for modeling mathematical programs, builds on existing MPI implementations to ensure efficiency and scalability, and is available via http://github.com/Pyomo/mpi-sppy.

97 MATHEMATICS AND COMPUTING↗

Electronic Structure Theory Calculations Using Modern Architectures: KNL vs Haswell

The time to solution and parallel efficiency of several commonly used electronic structure methods (Hartree–Fock, density functional theory, second order perturbation theory, resolution of the identity second order perturbation theory, coupled cluster) are evaluated on both the Intel Xeon Haswell and the Intel Xeon Phi Knights Landing (KNL) architectures. The Haswell completes the benchmark calculations with a faster time to solution than the KNL for all molecules and methods tested. While the Haswell exhibits an average speedup of at least 3.5 relative to the KNL for all nonthreaded computations, the KNL has a better parallel efficiency than the Haswell with increasing core counts. The architectures are further tested using a more computationally costly coupled cluster method on a transition state reaction. The Haswell appears to be the best choice to minimize the time to solution, though for very large systems and high levels of theory that require memory intensive processes the superior memory hierarchy and larger on node memory of the KNL can make it a better choice. These results are used to showcase aspects of novel architectures that will increase efficiency for quantum chemistry applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Paracousti v. 2.0.0

Paracousti simulates 3-D acoustic wave propagation in fixed (non-moving) complex media. It solves the linear acoustic equations of motion using the velocity-pressure system of first order linear differential equations on a finite-difference Cartesian grid using Newton’s law of motion and mass continuity equations. It also has the ability to incorporate acoustic attenuation to simulate non-recoverable energy losses via the velocity-memory-pressure system of linear differential equations. We assume stationary, non-heat conducting, adiabatic media (fluid) where the background sound speed and material density are fixed in time. Capabilities include massively parallel design, optimization for high contrast media interfaces, inclusion of arbitrary pressure and force sources defined by the user, inclusion of arbitrary pressure and velocity receivers defined by the user, acoustic wavefield snapshots in time for visualization, and convolutional perfectly matched layers to minimize artificial grid boundary reflections. Paracousti was built upon the foundational framework of TDAAPS (Time-Domain Atmospheric Acoustic Propagation Suite) by Neill Symons, Dave Aldridge, and Leiph Preston.

Preston, Leiph↗

plexos-coad (Plexos Class-Object-Attribute Data manipulation tool)

Clean energy systems including the future power grid are enabled via the development, analysis and application of advanced simulation of complex systems based on large datasets. The ability to handle and enable the simulation of complex systems allows researchers and analysts to address significant problems with greater confidence and greater levels of integrity. Parallel execution of complex systems is paramount to addressing increasing complexity. Programmatic interfaces for software configuration and parallel execution enable handling greater complexity and improving simulation integrity. The Class Object Attribute Data (COAD) software is written as a programmatic interface to the PLEXOS dataset that enables the decomposition of the dataset in time and execution in parallel without loss of integrity. COAD also enable the recomposition of solution datasets that are the output of distributed parallel execution of the core simulator.

Jones, Wes↗

Optimization and Augmentation for Data Parallel Contour Trees

Contour trees are used for topological data analysis in scientific visualization. While originally computed with serial algorithms, recent work has introduced a vector-parallel algorithm. Furthermore, this algorithm is relatively slow for fully augmented contour trees which are needed for many practical data analysis tasks. We therefore introduce a representation called the hyperstructure that enables efficient searches through the contour tree and use it to construct a fully augmented contour tree in data parallel, with performance on average 6 times faster than the state-of-the-art parallel algorithm in the TTK topological toolkit.

97 MATHEMATICS AND COMPUTING↗

On the use of a multigrid-reduction-in-time algorithm for multiscale convergence of turbulence simulations

Simulations of turbulent flow present challenges in terms of accuracy and affordability on modern highly-parallel computer architectures. A multigrid-reduction-in-time algorithm is used to provide a framework for separately evolving different scales of turbulence and for parallelizing the temporal domain, thereby increasing the concurrency. It is hypothesized that the space–time locality of the small scales of turbulence can be used to circumvent difficulties in applying temporal multigrid to flows dominated by inertial physics. For algorithms that fall well short of spectral accuracy (fourth-order is used in this work) attention must be paid to the accuracy of features on scales transferred between multigrid levels. Numerical experiments were performed using implicit large-eddy simulation. Results from applying the approach to an infinite-Reynolds number Taylor–Green flow and a double-shear flow at a Reynolds number of 11650 provide strong evidence that the approach has merit. The multigrid-reduction-in-time framework can be used to parallelize the temporal domain of a high-Reynolds-number turbulent flow and permit independent convergence of different scales. Establishing this foundation allows for future research in reducing the wall-clock time to solve turbulent flows while retaining the same accuracy as sequential solvers. In conclusion, current performance results from parallelizing the temporal domain are not competitive with those from sequential-in-time methods.

97 MATHEMATICS AND COMPUTING↗

Optimizing the Accelerated Recursive Doubling Algorithm for Block Tridiagonal Systems of Equations

The need to solve block tridiagonal systems with hundreds or thousands of right-hand sides for the same block tridiagonal matrix is common in a variety of disciplines. To meet this need, the Accelerated Recursive Doubling Algorithm was developed. After a right-hand side independent phase, the algorithm allows for the quick, online calculation of solutions for different right-hand sides. In this work, we present methods to optimize the Accelerated Recursive Doubling Algorithm in memory usage and computation time in a hybrid parallelization model. The right-hand side independent phase of the naïve implementation takes ≥ 11/3 the amount of memory required to store the tridiagonal matrix, while our implementation reduces the fraction to ≈ 5/3 . The right-hand side dependent phase of the naïve implementation takes ≥ 6 times the amount of memory required to store the right-hand side, while our implementation reduces the fraction to ≈ 3. The computation time for the independent phase is reduced to ≈ 2/3 times that of the naïve implementation, while the computation time for the dependent phase is reduced to ≈ 5/9 . With increasing numbers of shared-memory threads q on every distributed processing element, we have O(q) theoretical speedup.

97 MATHEMATICS AND COMPUTING↗

Understanding data motion in the modern HPC data center

The utilization and performance of storage, compute, and network resources within HPC data centers have been studied extensively, but much less work has gone toward characterizing how these resources are used in conjunction to solve larger scientific challenges. To address this gap, we present our work in characterizing workloads and workflows at a data-center-wide level by examining all data transfers that occurred between storage, compute, and the external network at the National Energy Research Scientific Computing Center over a three-month period in 2019. Using a simple abstract representation of data transfers, we analyze over 100 million transfer logs from Darshan, HPSS user interfaces, and Globus to quantify the load on data paths between compute, storage, and the wide-area network based on transfer direction, user, transfer tool, source, destination, and time. We show that parallel I/O from user jobs, while undeniably important, is only one of several major I/O workloads that occurs throughout the execution of scientific workflows. We also show that this approach can be used to connect anomalous data traffic to specific users and file access patterns, and we construct time-resolved user transfer traces to demonstrate that one can systematically identify coupled data motion for individual workflows.

Lockwood, GK↗

Advances in Multi-Physics Modeling for Parallel Finite Element Code Suite ACE3P

SLAC developed ACE3P code suite is a comprehensive set of parallel finite-element codes for multi-physics modeling of particle accelerators. Running on massively parallel computer platforms for high fidelity and high accuracy simulation, ACE3P enables rapid virtual prototyping of accelerator and RF component design, optimization and analysis. Furthermore, recent advances of ACE3P have been focused on the implementation of advanced numerical algorithms, enhancement of multi-physics capabilities, and improvement of code performance on state-of-the-art high performance computing (HPC) platforms for large-scale RF modeling in accelerator applications and beyond. In this paper, we will present a nonlinear electromagnetic (EM) eigensolver for damping calculation of resonant modes for cavities coupled with waveguides, the thermal solver for accurate evaluation of heat loads in superconducting RF (SRF) cavity power coupler, the elastic solver for investigation of SRF cavity cryomodule (CM) bowing due to thermal effect, the frequency domain mechanical solver for studying SRF cavity mechanical oscillation modes, the particle tracking code for dark current simulation in SRF CM using a hybrid MPI+OpenMP parallel programing model, the time domain solver for high fidelity modeling of EM wave propagation for medical device in human body.

97 MATHEMATICS AND COMPUTING↗