Recent Advances on GPU Computing in Operations Research

Nowadays graphics processing units (GPUs) have become popular parallel computing platforms known as General-Purpose GPU (GPGPU) computing. GPUs thereby are chosen by some security researchers as cryptographic accelerators to secure massive volumes of transactions. However, their security issues are ignored in spite of their popularity and performance. There are some possible information leakages faced with malicious attacks or even in the normal GPU computing. Our objective is to secure the confidentiality of cryptographic keys in GPU computing environments and provide easy-to-use programming with few constraints. In this paper, we propose a prototype in Linux, a system of GPGPU computing solution empowered by GPU virtualization technology, which keeps encrypted keys in guest machine to protect secret keys from leakage even in the event of full system compromise. With the API interception and redirection of CUDA, applications in Virtual Machines (VMs) can access the GPU device in a transparent way. Besides, we use virtio, a dedicated virtual I/O device, to transfer data between virtual and host machines in high performance. In our current study, we evaluate our prototype with the GPU implementation of ECC. We show that it can protect private keys of GPU cryptographic computation and it also incurs low performance penalty compared with the native environment, therefore demonstrating the prototype is secure and requires reasonable overhead.

Heterogeneous systems with both Central Processing Units (CPUs) and Graphics Processing Units (GPUs) are frequently used to accelerate short-ranged Molecular Dynamics (MD) simulations. The most time-consuming task in short-ranged MD simulations is the computation of particle-to-particle interactions. Beyond a certain distance, these interactions decrease to zero. To minimize the operations to investigate distance, previous works have tiled interactions by employing the spatial attribute, which increases the memory access and GPU computations, hence decreasing performance. Other studies ignore the spatial attribute and construct an all-versus-all interaction matrix, which has poor scalability. This paper presents an improved algorithm. The algorithm first bins particles into voxels according to the spatial attributes, and then tiles the all-versus-all matrix into voxel-versus-voxel sub-matrixes. Only the sub-matrixes between neighboring voxels are computed on the GPU. Therefore, the algorithm reduces the distance examine operations and limits additional memory access and GPU computations. This paper also adopts a multi-level programming model to implement the algorithm on multi-nodes of Tianhe-lA. By employing (1) a patch design to exploit parallelism across the simulation domain, (2) a communication overlapping method to overlap the communications between CPUs and GPUs, and (3) a dynamic workload balancing method to adjust the workloads among compute nodes, the implementation achieves a speedup of 4.16× on one NVIDIA Tesla M2050 GPU compared to a 2.93 GHz six-core Intel Xeon X5670 CPU. In addition, it runs 2.41× faster on 256 compute nodes of Tianhe-lA (with two CPUs and one GPU inside a node) than on 256 GPU-excluded nodes.

GPU acceleration of MPAS microphysics WSM6 using OpenACC directives: Performance and verification

Feedback control has become a crucial tool in the research on magnetic confinement of plasmas for achieving controlled nuclear fusion. This thesis presents a novel plasma feedback control system that, for the first time, employs a Graphics Processing Unit (GPU) for microsecond-latency, real-time control computations. This novel application area for GPU computing is opened up by a new system architecture that is optimized for low-latency computations on less than kilobyte sized data samples as they occur in typical plasma control algorithms. In contrast to traditional GPU computing approaches that target complex, high-throughput computations with massive amounts of data, the architecture presented in this thesis uses the GPU as the primary processing unit rather than as an auxiliary of the CPU, and data is transferred from A-D/D-A converters directly into GPU memory using peer-to-peer PCI Express transfers. The described design has been implemented in a new, GPU-based control system for the High-Beta Tokamak – Extended Pulse (HBT-EP) device. The system is built from commodity hardware and uses an NVIDIA GeForce GPU and D-TACQ A-D/D-A converters providing a total of 96 input and 64 output channels. The system is able to run with sampling periods down to 4 μs and latencies down to 8 μs. The GPU provides a total processing power of 1.5 x 1012 floating point operations per second. To illustrate the performance and versatility of both the general architecture and concrete implementation, a new control algorithm has been developed. The algorithm is designed for the control of multiple rotating magnetic perturbations in situations where the plasma equilibrium is not known exactly and features an adaptive system model: instead of requiring the rotation frequencies and growth rates embedded in the system model to be set a priori, the adaptive algorithm derives these parameters from the evolution of the perturbation amplitudes themselves. This results in non-linear control computations with high computational demands, but is handled easily by the GPU based system. Both digital processing latency and an arbitrary multi-pole response of amplifiers and control coils is fully taken into account for the generation of control signals. To separate sensor signals into perturbed and equilibrium components without knowledge of the equilibrium fields, a new separation method based on biorthogonal decomposition is introduced and used to derive a filter that performs the separation in real-time. The control algorithm has been implemented and tested on the new, GPU-based feedback control system of the HBT-EP tokamak. In this instance, the algorithm was set up to control four rotating n = 1 perturbations at different poloidal angles. The perturbations were treated as coupled in frequency but independent in amplitude and phase, so that the system effectively controls a helical n = 1 perturbation with unknown poloidal spectrum. Depending on the plasma's edge safety factor and rotation frequency, the control system is shown to be able to suppress the amplitude of the dominant 8 kHz mode by up to 60% or amplify the saturated amplitude by a factor of up to two. Intermediate feedback phases combine suppression and amplification with a speed up or slow down of the mode rotation frequency. Increasing feedback gain results in the excitation of an additional, slowly rotating 1.4 kHz mode without further effects on the 8 kHz mode. The feedback performance is found to exceed previous results obtained with an FPGA- and Kalman-filter based control system without requiring any tuning of system model parameters. Experimental results are compared with simulations based on a combination of the Boozer surface current model and the Fitzpatrick-Aydemir model. Within the subset of phenomena that can be represented by the model as well as determined experimentally, qualitative agreement is found.

Bioinspired methods usually need a high amount of computational resources. For this reason, parallelization is an interesting alternative in order to decrease the execution time and to provide accurate results. In this sense, recently there has been a growing interest in developing parallel algorithms using graphic processing units (GPU) also refered as GPU computation. Advances in the video gaming industry have led to the production of low-cost, high-performance graphics processing units (GPUs) that possess more memory bandwidth and computational capability than central processing units (CPUs). As GPUs are available in personal computers, and they are easy to use and manage through several GPU programming languages (CUDA, OpenCL, etc.), graphics engines are being adopted widely in scientific computing applications, particularly in the fields of computational biology and bioinformatics. This paper reviews the use of GPUs to solve scientific problems, giving an overview of current software systems.

My research in optimization at the Department of Systems and Computer Engineering at Carleton University has brought me into contact with researchers in the Department of Electronics, our sister department in the general field of Electrical and Computer Engineering (ECE), which has a major research thrust in computer-aided design (CAD) of very large scale integrated (VLSI) circuits. I have come to realize that the design of VLSI systems consists in large part of solving incredibly massive mixed-integer nonlinear optimization problems, together with enormous circuit simulations. This is impossible without the use of CAD techniques. Over time, ECE-CAD researchers have both borrowed useful standard techniques from operations research (OR) and have invented their own, often to deal with the sheer scale and complexity of the design problems they face. Interaction between the OR and ECE-CAD communities would seem to be a natural development. Coincidentally, the INFORMS Journal on Computing had an area entitled “High Performance Computation” that covered (i) the solution of OR problems using new computing technologies, (ii) the application of OR techniques in the design and use of highperformance computing and communication systems, and (iii) solution methods for ultra-large-scale OR applications. The viability of this area was debated during 2003 as some of its aspects migrated to other areas (e.g., the new “Telecommunications and Electronic Commerce” area), and the number of submissions declined. The area was eventually closed, although I argued that the overlap between OR and ECE-CAD, essentially covering items (ii) and (iii), was a very active research area. This Special Cluster of papers was conceived as a way to test that argument. I was recruited at the same time to prepare a tutorial on ECE-CAD for the 2004 INFORMS Annual Meeting (see John W. Chinneck, Michel Nakhla, and Q. J. Zhang 2004. Computer-aided design for electrical and computer engineering. H. J. Greenberg, ed. Tutorials on Emerging Methodologies and Applications in Operations Research. Springer, New York, 6-1 to 6-44). The preparation of the article reinforced my observation about the research overlap between OR and ECE-CAD. A search of the electrical engineering literature for 2000 through early 2004 turned up 46,725 papers mentioning “simulate” or “simulation” as keywords in the abstract, 14,216 papers mentioning “optimization” or “optimize,” and relatively smaller numbers for specific techniques such as “neural network” (6,251), “genetic algorithm” (2,603), “linear programming” (576), “simulated annealing” (448), and “branch and bound” (199). One surprise was the relatively small number of papers using the generic keywords “mathematical programming” (68) or “operations research” (37). The general conclusion of the tutorial article is that the OR and the ECE-CAD communities have much to offer each other. This is certainly the case for the papers gathered in this Special Cluster. We see known OR techniques adapted for use in ECECAD. In “Integer Linear Programming Models for Global Routing,” Behjat et al. apply integer linear programming in a heuristic to solve enormous NPhard connection routing problems for VLSI circuits. In “Task Scheduling in a Finite-Resource, Reconfigurable Hardware/Software Codesign Environment,” Loo and Wells use simulated annealing, genetic algorithms, and random search techniques to solve scheduling problems in hardware-software co-design. We also see new techniques specifically developed by the ECE-CAD community to deal with problems of extreme scale. In “A Projection-Based Reduction Approach to Computing Sensitivity of Steady-State Response of Nonlinear Circuits,” Pai et al. develop methods for sensitivity analysis in extremely large nonlinear programs, especially those in which the objective function is very costly to evaluate. The methods have special relevance for simulation-based

A high-order spectral difference (SD) method has been developed with graphics processing units (GPUs) using compute unified device architecture (CUDA). It solves the three-dimensional Navier-Stokes equations on unstructured hexahedral grids with RungeKutta time integration. The method is efficient since operations are completed in a onedimensional fashion and the equations are solved in differential form, removing explicit surface and volume integral calculations. Additionally, solution and flux reconstructions are completed locally per cell, increasing the parallelization of the implementation. Due to this efficiency, the application of GPU computing is appealing. This paper presents the SD method implementation with GPU CUDA computing and presents accuracy studies with isotropic vortex propagation and Couette flow, verifies the high-order accuracy of the solver with a numerical sensitive aero-acoustic problem, and compares the developed solver and a high-order finite difference solver with a case presented in the 1st International Workshop on High-Order CFD Methods. Finally, the GPU solver is compared to a similar central processing unit (CPU) solver, where speed-ups ranging from 20-40x faster are illustrated.

Purpose:The calculation time is a trade‐off for improving the accuracy of convolution dose calculation with fine calculation spacing of the KERMA kernel. We investigated to accelerate the convolution calculation using an ideal kernel on the Graphic Processing Units (GPU).Methods:The calculation was performed on the AMD graphics hardware of Dual FirePro D700 and our algorithm was implemented using the Aparapi that convert Java bytecode to OpenCL. The process of dose calculation was separated with the TERMA and KERMA steps. The dose deposited at the coordinate (x, y, z) was determined in the process. In the dose calculation running on the central processing unit (CPU) of Intel Xeon E5, the calculation loops were performed for all calculation points. On the GPU computation, all of the calculation processes for the points were sent to the GPU and the multi‐thread computation was done. In this study, the dose calculation was performed in a water equivalent homogeneous phantom with 1503 voxels (2 mm calculation grid) and the calculation speed on the GPU to that on the CPU and the accuracy of PDD were compared.Results:The calculation time for the GPU and the CPU were 3.3 sec and 4.4 hour, respectively. The calculation speed for the GPU was 4800 times faster than that for the CPU. The PDD curve for the GPU was perfectly matched to that for the CPU.Conclusion:The convolution calculation with the ideal kernel on the GPU was clinically acceptable for time and may be more accurate in an inhomogeneous region. Intensity modulated arc therapy needs dose calculations for different gantry angles at many control points. Thus, it would be more practical that the kernel uses a coarse spacing technique if the calculation is faster while keeping the similar accuracy to a current treatment planning system.

Graphics processing units (GPUs) have been widely adopted to accelerate the training of deep neural networks (DNNs). Although the computational performance of GPUs has been improving steadily, the memory size of modern GPUs is still quite limited, which restricts the sizes of DNNs that can be trained on GPUs, and hence raises serious challenges. This paper introduces a framework, referred to as moDNN (memory optimal DNN training on GPUs), to optimize the memory usage in DNN training. moDNN supports automatic tuning of DNN training code to match any given memory budget (not smaller than the theoretical lower bound). By taking full advantage of overlapping computations and data transfers, we develop new heuristics to judiciously schedule data offloading and prefetching transfers, together with convolution algorithm selection, to optimize memory usage. We further devise a new sub-batch size selection method which also greatly reduces memory usage. moDNN can save memory usage up to 59×, compared with an ideal case which assumes that the GPU memory is sufficient to hold all data. When executing moDNN on a GPU with 12 GB memory, the training time is increased by only 3 percent, which is much shorter than that incurred by the best known approach, vDNN. Furthermore, we propose an optimization strategy for moDNN on multiple GPUs again by utilizing the idea of overlapping data transfers and GPU computations. The results show that 3.7× speedup is attained on four GPUs.

With the rising number of application accelerators, developers are looking for ways to evaluate new and competing platforms quickly, fairly, and early in the development cycle. As high-performance computing (HPC) applications increase their demands on application acceleration platforms, graphics processing units (GPUs) provide a potential solution for many developers looking for increased performance. Device performance metrics, such as Computational Density (CD), provide a useful but limited starting point for device comparison. The authors developed the Realizable Utilization (RU) metric and methodology to quantify the discrepancy between theoretical device performance shown by CD and the performance developers can achieve. As the RU score increases, the application is achieving a larger percentage of the computational power the device can provide. The authors survey technical publications about GPUs and use this data to analyze the RU scores for several arithmetic application kernels that are frequently accelerated in GPUs. The RU concepts presented in this paper are a first step towards a formalized comparison framework for diverse devices such as CPUs, FPGAs, GPUs and other novel architectures. GPU kernels for matrix multiplication, matrix decomposition, and N-body simulations show RU scores ranging from almost 0% to approaching 99% depending on the application, but all kernel areas show a significant decrease in RU as the computational capacities increase. Additionally, the RU scores show the higher realized performance of the GeForce 8 Series GPUs versus newer GPU architectures. This paper shows that applications running on GPUs with higher computational density report significantly lower RU scores than more mature GPUs with lower computational density. This trend implies that while the raw performance available is still increasing with newer GPUs, the achieved performance is not keeping pace with the theoretical capacities of the devices.

Multi-Agent Systems (MAS) can be used to model systems where the global behavior cannot be uniformly represented by standard techniques such as partial differential equations or linear systems because the system elements have their own independent behavior. This is, for instance, the case in complex systems such as daily mobility in a city for example. Depending on the system size the computing power needs for the MAS may be as big as for more traditional linear numerical systems and may need to be parallelized to fully represent real systems. Graphical Processing Units (GPU) have already proven to be an efficient support to execute large linear programs. In this paper we present the use of GPU for the execution of Sworm, a multi-scale MAS system. We show that GPU computing can be efficient in that less regular case and when the agent behavior is simple. We advocate for a wider use of the GPU in Agent Based Models in particular for multi-scale systems with work distribution between the CPU and GPU.

This contribution deals with the Austrian research project AURORA and the application of high performance computing (HPC) in the field of microelectronics. In the first part the ‘Spezialforschungsbereich’ AURORA - Advanced Models, Applications, and Software Systems for High Performance Computing - is presented which is funded by the Austrian ‘Fonds zur Forderung der wissenschaftlichen Forschung’. Seven research groups belonging to different institutes of the ‘Universitat Wien’ and the ‘Technische Universitat Wien’ are participating in AURORA, thus covering the fields computer science, statistics and operations research, numerical mathematics, electrochemistry, and microelectronics. The second part deals with the activities concerning the application of HPC to the simulation of the behaviour of microelectronic devices and their technological process steps in order to intensify the research capabilities of the simulation tools.

Data in a data center are stored dispersively. The data-oriented task computing disperses big data analysis tasks to different computing nodes. The extensive use of graphics processing unit (GPU) makes it urgent and important to study how to reasonably assign heterogeneous resources to different computing frameworks. We investigate the existing big data computing framework and the GPU computing. Based on the existing cluster resource management model and the GPU management model, we propose a hybrid heterogeneous resource management model that combines CPU resources with GPU resources. The computing nodes manage local resources and implement tasks; the resource management center concertedly manage various computing frameworks. We design and implement a hybrid domain resource sharing and allocation algorithm, which allocates the hybrid domain resources to computing frameworks according to the coordinated use of them so as to fairly share the hybrid domain resources among various computing frameworks and prevent the CPU from too many tasks but the GPU or CPU from resource "hunger". The experimental results show that the allocation algorithm can increase the use of heterogeneous resources and the number of completed tasks by around 15%.

Graphic Processing Units (GPUs) have become the accelerator of choice for improving the performance of many of the most demanding applications. While performance of these devices continues to improve generation after generation, reliability of these devices has not been studied rigorously. Several sources of errors can undermine the reliability of these devices, including radiation-induced transient faults, environmental perturbations, and process, temperature or voltage variations. In particular, transient faults in GPU execution have become a significant threat to high performance computing (HPC) and safety-critical applications. HPC systems experience transient faults every few tens of hours and the trend is expected to become worse. A key point in the study of transient faults and their effects on user programs is that some faults do not cause undesirable results in the affected programs. This is especially true for GPU applications. Past efforts to study and understand GPU vulnerability to transient faults have demonstrated reliability can vary greatly across different applications. A significant amount of resilience resides intrinsically in some GPU applications. Transient faults in these applications are not likely to affect the results they produce. Other applications are highly sensitive to transient faults and are likely to crash or produce incorrect results when they are affected by transient faults. While it is generally a good idea to protect the GPU hardware from transient faults, the penalties incurred in terms of performance, power and area are not always justifiable, depending on the applications utilizing the hardware resources. Understanding the relationship between the underlying program characteristics and their implications on vulnerability is crucial. The inherent resilience in applications should be carefully considered when making decisions about designing protection mechanisms to guard against nefarious transient faults. In this thesis, we focus on program characteristics that contribute to their vulnerability. We offer several methodologies that aim at alleviating the prohibitively expensive process of quantifying and estimating the vulnerability of GPU applications, as this is the first step toward improving the reliability of GPUs. Our analyses also demonstrate that beyond the variability between the vulnerabilities of different applications, the vulnerability of GPU applications also varies during their runtime, and present a phase behavior. This phase behavior opens new opportunities for not only more efficient vulnerability estimation, but also more efficient fault mitigation approaches. We demonstrate a methodology for application designers to reduce the cost of protection against transient faults.

SummaryAn OpenACC directive‐based graphics processing unit (GPU) parallel scheme is presented for solving the compressible Navier–Stokes equations on 3D hybrid unstructured grids with a third‐order reconstructed discontinuous Galerkin method. The developed scheme requires the minimum code intrusion and algorithm alteration for upgrading a legacy solver with the GPU computing capability at very little extra effort in programming, which leads to a unified and portable code development strategy. A face coloring algorithm is adopted to eliminate the memory contention because of the threading of internal and boundary face integrals. A number of flow problems are presented to verify the implementation of the developed scheme. Timing measurements were obtained by running the resulting GPU code on one Nvidia Tesla K20c GPU card (Nvidia Corporation, Santa Clara, CA, USA) and compared with those obtained by running the equivalent Message Passing Interface (MPI) parallel CPU code on a compute node (consisting of two AMD Opteron 6128 eight‐core CPUs (Advanced Micro Devices, Inc., Sunnyvale, CA, USA)). Speedup factors of up to 24× and 1.6× for the GPU code were achieved with respect to one and 16 CPU cores, respectively. The numerical results indicate that this OpenACC‐based parallel scheme is an effective and extensible approach to port unstructured high‐order CFD solvers to GPU computing. Copyright © 2015 John Wiley & Sons, Ltd.