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At least 1,459 records · Page 81

Distributed memory, GPU accelerated Fock construction for hybrid, Gaussian basis density functional theory

With the growing reliance of modern supercomputers on accelerator-based architecture such a graphics processing units (GPUs), the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority. While significant strides have been made in the development GPU accelerated, distributed memory algorithms for many modern electronic structure methods, the primary focus of GPU development for Gaussian basis atomic orbital methods has been for shared memory systems with only a handful of examples pursing massive parallelism. Here in this work, we present a set of distributed memory algorithms for the evaluation of the Coulomb and exact exchange matrices for hybrid Kohn–Sham DFT with Gaussian basis sets via direct density-fitted (DF-J-Engine) and seminumerical (sn-K) methods, respectively. The absolute performance and strong scalability of the developed methods are demonstrated on systems ranging from a few hundred to over one thousand atoms using up to 128 NVIDIA A100 GPUs on the Perlmutter supercomputer.

97 MATHEMATICS AND COMPUTING↗

An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

Here, we demonstrate use of a modern Fortran solver interface to manage solver algorithms for an implicit barotropic mode solver in the Model for Predictions Across Scales-Ocean (MPAS-O). ForTrilinos, a Fortran interface to Trilinos that contains a large collection of solver capabilities written in C++, has been implemented in MPAS-O to provide access to a suite of linear solver options. By virtue of the simplified wrapper and interface generator (SWIG) automation tool that generates modern Fortran interfaces to C++ code, we were able to implement the Fortran solver interface in MPAS-O using a familiar Fortran coding style while minimizing performance degradation. The ForTrilinos solver interface is written within MPAS-O’s time stepping modules as a subroutine in conjunction with MPAS-O code. Applied to an idealized ocean and a high-resolution realistic ocean test case, parallel performance of ForTrilinos solvers is examined. It is found that parallel scalability of the ForTrilinos solvers is highly dependent on the number of global synchronization points per solver iteration in each iterative solver algorithm. ForTrilinos solvers perform best compared to the Fortran hand-crafted (FHC) solver when the amount of work per processor is large enough. However, parallel scalability is better with the FHC solver and so when the work per core is modest FHC outperforms ForTrilinos. The intercomparison between the ForTrilinos and FHC solvers reveals that this performance hit in the ForTrilinos solver mostly comes from the global synchronization process, while suggesting that the matrix-vector multiplication process in the FHC solver needs to be optimized for better performance.

97 MATHEMATICS AND COMPUTING↗

The DEAL.II finite element library: Design, features, and insights

DEAL.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. In this paper, we outline its primary design considerations and its sophisticated features such as distributed meshes, h p -adaptivity, support for complex geometries, and matrix-free algorithms. But DEAL.II is more than just a software library: It is also a diverse and worldwide community of developers and users, as well as an educational platform. We therefore also discuss some of the technical and social challenges and lessons learned in running a large community software project over the course of two decades.

97 MATHEMATICS AND COMPUTING↗

Insight into 3D micro-CT data: exploring segmentation algorithms through performance metrics

Three-dimensional (3D) micro-tomography (µ-CT) has proven to be an important imaging modality in industry and scientific domains. Understanding the properties of material structure and behavior has produced many scientific advances. An important component of the 3D µ-CT pipeline is image partitioning (or image segmentation), a step that is used to separate various phases or components in an image. Image partitioning schemes require specific rules for different scientific fields, but a common strategy consists of devising metrics to quantify performance and accuracy. The present article proposes a set of protocols to systematically analyze and compare the results of unsupervised classification methods used for segmentation of synchrotron-based data. Additionally, the proposed dataflow for Materials Segmentation and Metrics (MSM) provides 3D micro-tomography image segmentation algorithms, such as statistical region merging (SRM), k-means algorithm and parallel Markov random field (PMRF), while offering different metrics to evaluate segmentation quality, confidence and conformity with standards. Both experimental and synthetic data are assessed, illustrating quantitative results through the MSM dashboard, which can return sample information such as media porosity and permeability. The main contributions of this work are: (i) to deliver tools to improve material design and quality control; (ii) to provide datasets for benchmarking and reproducibility; (iii) to yield good practices in the absence of standards or ground-truth for ceramic composite analysis.

97 MATHEMATICS AND COMPUTING↗

MILC staggered conjugate gradient performance on Intel KNL

We review our work done to optimize the staggered conjugate gradient (CG) algorithm in the MILC code for use with the Intel Knights Landing (KNL) architecture. KNL is the second gener- ation Intel Xeon Phi processor. It is capable of massive thread parallelism, data parallelism, and high on-board memory bandwidth and is being adopted in supercomputing centers for scientific research. The CG solver consumes the majority of time in production running, so we have spent most of our effort on it. We compare performance of an MPI+OpenMP baseline version of the MILC code with a version incorporating the QPhiX staggered CG solver, for both one-node and multi-node runs.

97 MATHEMATICS AND COMPUTING↗

Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and electronic gap of rutile titania nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Angstrom (24 atoms) to 10.3 Angstrom (384 atoms) using a highly-parallel real-space DFT code to enable hybrid level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy, and evaluate the influence of defects on electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Angstrom. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS is highly dependent on the shape and size of these particles. Furthermore, the DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigen value distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermochimica User Manual – v1.0

A new software library called Thermochimica has been developed that determines a unique combination of phases and their compositions at thermochemical equilibrium. The development of Thermochimica in this research is aimed at direct integration in multi-physics codes and to address several concerns with using commercially available software, including: licensing entanglements associated with code distribution, access to the source code, convenient incorporation into other codes with quality assurance considerations, and computational performance. In particular, significant research efforts have been dedicated to enhance computational performance through advanced algorithm development, such as improved estimation techniques and non-linear solvers. The overall goal of this undertaking is to provide an open source computational tool to enhance the predictive capability of multiphysics codes without significantly impeding computational performance. The purpose of this document is to describe the design of Thermochimica and the basic use of the software library. A brief background to computational thermodynamics and the conditions for thermodynamic equilibrium is given in §2, details of the code development is discussed in §3, details of building and compiling Thermochimica is given in §4, specific programming details for each subroutine in the library is given in the Appendix. The open license for Thermochimica is provided with the source code. As is always the case, software quality assurance (SQA) is an extremely important subject in software development. The importance of this warrants an independent document dedicated to SQA, which has been developed in parallel to this document. The subject of thermodynamic model validation is also of extreme importance in scientific computing and must be given careful attention. To be clear, this document is concerned with the development and use of a general thermodynamic solver and the validation of any models should be included in the discussion of the development of a thermodynamic model that is specific to a particular system.

36 MATERIALS SCIENCE↗

Closed-Loop Error Learning Control for Uncertain Nonlinear Systems With Experimental Validation on a Mobile Robot

This article develops a closed-loop error learning control (CLELC) algorithm for feedback linearizable systems with experimental validation on a mobile robot. Traditional feedback and feedforward controllers are designed based on the nominal model by using the feedback linearization control (FLC) method. Then, an intelligent controller is designed based on the sliding mode learning algorithm that utilizes closed-loop error dynamics to learn the system behavior. The controllers are working in parallel, and the intelligent controller can gradually replace the feedback controller from the control of the system. In addition to the stability of the sliding mode learning algorithm, the closed-loop stability of an nth-order feedback linearizable system is proven. The simulation results demonstrate that the CLELC algorithm can improve control performance (e.g., smaller rise time, settling time, and overshoot) in the absence of uncertainties, and also provides robust control performance in the presence of uncertainties as compared to traditional FLC method. To test the efficiency and efficacy of the CLELC algorithm, the trajectory tracking problem of a tracked mobile robot is studied in real time. The experimental results demonstrate that the CLELC algorithm ensures highly accurate trajectory tracking performance than traditional FLC method.

97 MATHEMATICS AND COMPUTING↗

Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.

Bayesian optimization↗

Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration

Turbulent Richtmyer–Meshkov instability (RMI) is investigated through a series of high resolution three-dimensional simulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regimes combined. Overall, the growth rate exponent is determined as θ=0.292±0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is shown to be relatively insensitive to the choice of mixing layer width measurements. The asymptotic integral molecular mixing measures Θ=0.792±0.014, Ξ=0.800±0.014, and Ψ=0.782±0.013 are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49% and 66% higher kinetic energy in the shock parallel direction compared to perpendicular and does not show any return to isotropy. The plane averaged volume fraction profiles at different time instants collapse reasonably well when scaled by the integral width, implying that the layer can be described by a single length scale and thus a single θ. In conclusion, quantitative data given for both ensemble averages and individual algorithms provide useful benchmark results for future research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

True Load Balancing for Matricized Tensor Times Khatri-Rao Product

MTTKRP is the bottleneck operation in algorithms used to compute the CP tensor decomposition. For sparse tensors, utilizing the compressed sparse fibers (CSF) storage format and the CSF-oriented MTTKRP algorithms is important for both memory and computational efficiency on distributed-memory architectures. Existing intelligent tensor partitioning models assume the computational cost of MTTKRP to be proportional to the total number of nonzeros in the tensor. However, this is not the case for the CSF-oriented MTTKRP on distributed-memory architectures. We outline two deficiencies of nonzero-based intelligent partitioning models when CSF-oriented MTTKRP operations are performed locally: failure to encode processors' computational loads and increase in total computation due to fiber fragmentation. We focus on existing fine-grain hypergraph model and propose a novel vertex weighting scheme that enables this model encode correct computational loads of processors. We also propose to augment the fine-grain model by fiber nets for reducing the increase in total computational load via minimizing fiber fragmentation. In this way, the proposed model encodes minimizing the load of the bottleneck processor. In conclusion, parallel experiments with real-world sparse tensors on up to 1024 processors prove the validity of the outlined deficiencies and demonstrate the merit of our proposed improvements in terms of parallel runtimes.

97 MATHEMATICS AND COMPUTING↗

mystic - a brief introduction

The mystic framework enables the solving of difficult optimization problems through three major innovations: (1) plug-and-play component-based optimization algorithms, (2) the ability to dynamically construct and apply generalzed trnasforms, K , where x' = K(x) , and (3) workflows providing asynchronous execution and statefulness. These features, in conjunction with supporting packages pathos , pyina , and klepto , can provide massively-parallel scalable workflows for quickly solving optimization problems in complex nonlinear spaces. mystic can be used to simplify non-convex optimization problems by transforming away nonlinearities through user-built kernel transforms. This tutorial demonstrates using mystic for machine learning with automated dimensional-reduction, using embarrasingly parallel solver ensembles to find an accurate interpolated surrogate for a nonlinear surface, and the determination of worst-case bounds on expectation value of an objective function under uncertainty.

97 MATHEMATICS AND COMPUTING↗

Energy-efficient mapping of large-scale workflows under deadline constraints in big data computing systems

Large-scale workflows for big data analytics have become a main consumer of energy in data centers where moldable parallel computing models such as MapReduce are widely applied to meet high computational demands with time-varying computing resources. The granularity of task partitioning in each moldable job of such big data workflows has a significant impact on energy efficiency, which remains largely unexplored. In this paper, we analyze the properties of moldable jobs and formulate a workflow mapping problem to minimize the dynamic energy consumption of a given workflow request under a deadline constraint in big data systems. Since this problem is strongly NP-hard, we design a fully polynomial-time approximation scheme (FPTAS) for a special case with a pipeline-structured workflow on a homogeneous cluster and a heuristic for the generalized problem with an arbitrary workflow on a heterogeneous cluster. The performance superiority of the proposed solution in terms of dynamic energy saving and deadline missing rate is illustrated by extensive simulation results in comparison with existing algorithms, and further validated by real-life workflow implementation and experimental results in Hadoop/YARN systems.

97 MATHEMATICS AND COMPUTING↗

3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba's simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi et al, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Furthermore, our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

PMU-Based Decoupled State Estimation for Unsymmetrical Power Systems

Modal decomposition of measurement equations has already been shown to simplify the formulation and resulting computational complexity of three-phase state estimation of systems where all the transmission lines are three-phase and fully transposed. When there are non-transposed and/or mixed-phase lines, modal decomposition can no longer fully decouple the threephase measurement equations. Here, this paper addresses the above shortcoming by proposing a simple yet practical solution based on the commonly used numerical compensation techniques. Thus, it enables application of the powerful decoupling approach to any type of three-phase networks which may contain non-transposed or mixed-phase lines and are fully observable by PMUs. The proposed procedure modifies the measurement set by deriving additive terms that compensate for the neglected unsymmetrical effects. It will be shown that unbalanced systems including nontransposed and mixed-phase elements, can still be transformed into three decoupled subsystems and solved in parallel by the proposed approach. Performance of the proposed algorithm is validated against several IEEE test cases.

42 ENGINEERING↗

A Work-Efficient Parallel Sparse Matrix-Sparse Vector Multiplication Algorithm

We design and develop a work-efficient multithreaded algorithm for sparse matrix-sparse vector multiplication (SpMSpV) where the matrix, the input vector, and the output vector are all sparse. SpMSpV is an important primitive in the emerging GraphBLAS standard and is the workhorse of many graph algorithms including breadth-first search, bipartite graph matching, and maximal independent set. As thread counts increase, existing multithreaded SpMSpV algorithms can spend more time accessing the sparse matrix data structure than doing arithmetic. Our shared-memory parallel SpMSpV algorithm is work efficient in the sense that its total work is proportional to the number of arithmetic operations required. The key insight is to avoid each thread individually scan the list of matrix columns. Our algorithm is simple to implement and operates on existing column-based sparse matrix formats. It performs well on diverse matrices and vectors with heterogeneous sparsity patterns. A high-performance implementation of the algorithm attains up to 15x speedup on a 24-core Intel Ivy Bridge processor and up to 49x speedup on a 64-core Intel KNL manycore processor. In contrast to implementations of existing algorithms, the performance of our algorithm is sustained on a variety of different input types include matrices representing scale-free and high-diameter graphs.

97 MATHEMATICS AND COMPUTING↗

Elastic Solutions to 2D Plane Strain Problems: Nonlinear Contact and Settlement Analysis for Shallow Foundations

The classical Neumann boundary value problem of an isotropic, homogeneous elastic half-plane under plane strain conditions is readdressed as the limiting case of the fully three-dimensional problem. Analytical solutions of the stress and strain tensors are obtained by taking the limit from known three-dimensional solutions. It is shown that the displacement fields for the plane strain problem are not well defined. A small number of simple expressions are developed, which provide a general solution for linearly-varying traction over arbitrary regions on the boundary. A simple, efficient, and rapidly convergent algorithm is developed which uses these solutions as analytic elements and provides a solution approach to the general boundary value problem. The method is verified against known solutions for Hertzian contact between parallel cylinders. Two numerical examples are presented for the analysis of shallow foundation systems. In the first, the boundary conditions are informed by analytical elastoplastic calculations and a strain influence analysis is performed and compared with the Schmertmann method. Subsequently, empirical laboratory contact traction distributions measured by Bauer et al., in both the normal and tangential directions are employed as boundary conditions for an analysis of the underlying stress field.

42 ENGINEERING↗

A GENERALIZED STOCHASTIC COLLOCATION APPROACH TO CONSTRAINED OPTIMIZATION FOR RANDOM DATA IDENTIFICATION PROBLEMS

We present a scalable, parallel mechanism for stochastic identification/control for problems constrained by partial differential equations with random input data. Several identification objectives will be discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $L^p$ norm, and the distributed parameters/control can both deterministic or stochastic. Given an objective we prove the existence of an optimal solution, establish the validity of the Lagrange multiplier rule and obtain a stochastic optimality system of equations. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the quantity of interest in each individual dimension. Hence, we introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system, where at each collocation point, deterministic analysis and techniques can be utilized. The advantage of our approach is that it allows for the optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of the input random fields, given the probability distribution of some responses of the system (quantities of physical interest). Our rigorously derived error estimates, for the fully discrete problems, will be described and used to compare the efficiency of the method with several other techniques. Numerical examples illustrate the theoretical results and demonstrate the distinctions between the various stochastic identification objectives.

Webster, Clayton G↗