m-CUBES: An Efficient and Portable Implementation of Multi-Dimensional Integration for GPUs

The task of multi-dimensional numerical integration is frequently encountered in physics and other scientific fields, e.g., in modeling the effects of systematic uncertainties in physical systems and in Bayesian parameter estimation. Multi-dimensional integration is often time-prohibitive on CPUs. Efficient implementation on many-core architectures is challenging as the workload across the integration space cannot be predicted a priori. We propose m-Cubes, a novel implementation of the well-known Vegas algorithm for execution on GPUs. Vegas transforms integration variables followed by calculation of a Monte Carlo integral estimate using adaptive partitioning of the resulting space. mCubes improves performance on GPUs by maintaining relatively uniform workload across the processors. As a result, our optimized Cuda implementation for Nvidia GPUs outperforms parallelization approaches proposed in past literature. We further demonstrate the efficiency of m-Cubes by evaluating a six-dimensional integral from a cosmology application, achieving significant speedup and greater precision than the Cuba library’s CPU implementation of Vegas. We also evaluate mCubes on a standard integrand test suite. m-Cubes outperforms the serial implementations of the Cuba and Gsl libraries by orders of magnitude speedup while maintaining comparable accuracy. Our approach yields a speedup of at least 10 when compared against publicly available Monte Carlo based GPU implementations. In summary, m-Cubes can solve integrals that are prohibitively expensive using standard libraries and custom implementations. A modern C++ interface header-only implementation makes m-Cubes portable, allowing its utilization in complicated pipelines with easy to define stateful integrals. Compatibility with non-Nvidia GPUs is achieved with our initial implementation of m-Cubes using the Kokkos framework

Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196

Efficient Machine Learning Approach for Optimizing Scientific Computing Applications on Emerging HPC Architectures

Efficient parallel implementations of scientific applications on multi-core CPUs with accelerators such as GPUs and Xeon Phis is challenging. This requires - exploiting the data parallel architecture of the accelerator along with the vector pipelines of modern x86 CPU architectures, load balancing, and efficient memory transfer between different devices. It is relatively easy to meet these requirements for highly-structured scientific applications. In contrast, a number of scientific and engineering applications are unstructured. Getting performance on accelerators for these applications is extremely challenging because many of these applications employ irregular algorithms which exhibit data-dependent control-flow and irregular memory accesses. Furthermore, these applications are often iterative with dependency between steps, and thus making it hard to parallelize across steps. As a result, parallelism in these applications is often limited to a single step. Numerical simulation of charged particles beam dynamics is one such application where the distribution of work and memory access pattern at each time step is irregular. Applications with these properties tend to present significant branch and memory divergence, load imbalance between different processor cores, and poor compute and memory utilization. Prior research on parallelizing such irregular applications have been focused around optimizing the irregular, data-dependent memory accesses and control-flow during a single step of the application independent of the other steps, with the assumption that these patterns are completely unpredictable. We observed that the structure of computation leading to control-flow divergence and irregular memory accesses in one step is similar to that in the next step. It is possible to predict this structure in the current step by observing the computation structure of previous steps. In this dissertation, we present novel machine learning based optimization techniques to address the parallel implementation challenges of such irregular applications on different HPC architectures. In particular, we use supervised learning to predict the computation structure and use it to address the control-flow and memory access irregularities in the parallel implementation of such applications on GPUs, Xeon Phis, and heterogeneous architectures composed of multi-core CPUs with GPUs or Xeon Phis. We use numerical simulation of charged particles beam dynamics simulation as a motivating example throughout the dissertation to present our new approach, though they should be equally applicable to a wide range of irregular applications. The machine learning approach presented here use predictive analytics and forecasting techniques to adaptively model and track the irregular memory access pattern at each time step of the simulation to anticipate the future memory access pattern. Access pattern forecasts can then be used to formulate optimization decisions during application execution which improves the performance of the application at a future time step based on the observations from earlier time steps. In heterogeneous architectures, forecasts can also be used to improve the memory performance and resource utilization of all the processing units to deliver a good aggregate performance. We used these optimization techniques and anticipation strategy to design a cache-aware, memory efficient parallel algorithm to address the irregularities in the parallel implementation of charged particles beam dynamics simulation on different HPC architectures. Experimental result using a diverse mix of HPC architectures shows that our approach in using anticipation strategy is effective in maximizing data reuse, ensuring workload balance, minimizing branch and memory divergence, and in improving resource utilization

Simulations of Coherent Synchrotron Radiation on Parallel Hybrid GPU/CPU Platform

Coherent synchrotron radiation (CSR) is an effect of self-interaction of an electron bunch as it traverses a curved path. It can cause a significant emittance degradation, as well as fragmentation and microbunching. Numerical simulations of the 2D/3D CSR effects have been extremely challenging due to computational bottlenecks associated with calculating retarded potentials via integrating over the history of the bunch. We present a new high-performance 2D, particle-in-cell code which uses massively parallel multicore GPU/GPU platforms to alleviate computational bottlenecks. The code formulates the CSR problem from first principles by using the retarded scalar and vector potentials to compute the self-interaction fields. The speedup due to the parallel implementation on GPU/CPU platforms exceeds three orders of magnitude, thereby bringing a previously intractable problem within reach. The accuracy of the code is verified against analytic 1D solutions (rigid bunch) and semi-analytic 2D solutions for the chirped bunch. Finally, we use the new code in conjunction with a genetic algorithm to optimize the design of a fiducial chicane

Fast algorithm for real-time rings reconstruction

The GAP project is dedicated to study the application of GPU in several contexts in which real-time response is important to take decisions. The definition of real-time depends on the application under study, ranging from answer time of μs up to several hours in case of very computing intensive task. During this conference we presented our work in low level triggers [1] [2] and high level triggers [3] in high energy physics experiments, and specific application for nuclear magnetic resonance (NMR) [4] [5] and cone-beam CT [6]. Apart from the study of dedicated solution to decrease the latency due to data transport and preparation, the computing algorithms play an essential role in any GPU application. In this contribution, we show an original algorithm developed for triggers application, to accelerate the ring reconstruction in RICH detector when it is not possible to have seeds for reconstruction from external trackers

Enhancing Energy Production with Exascale HPC Methods

High Performance Computing (HPC) resources have become the key actor for achieving more ambitious challenges in many disciplines. In this step beyond, an explosion on the available parallelism and the use of special purpose processors are crucial. With such a goal, the HPC4E project applies new exascale HPC techniques to energy industry simulations, customizing them if necessary, and going beyond the state-of-the-art in the required HPC exascale simulations for different energy sources. In this paper, a general overview of these methods is presented as well as some specific preliminary results.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the Intel Corporation, which enabled us to obtain the presented experimental results in uncertainty quantification in seismic imagingPostprint (author's final draft

Proceedings, MSVSCC 2014

Proceedings of the 8th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 17, 2014 at VMASC in Suffolk, Virginia