GPU-based Implementation Research Articles

Fractal-based supervised approach for dimensionality reduction of hyperspectral images

Dimensionality reduction is one of the most challenging and crucial issues apart from data mining, security, and scalability, which have retained much traction due to the ever-growing need to analyze the large volumes of data generated daily. Fractal Dimension (FD) has been successfully used to characterize data sets and has found relevant applications in dimension reduction. This paper presents an application of the FD Reduction (FDR) Algorithm on geospatial hyperspectral data, examining its usefulness for data sets with a relatively high embedding dimension. We examine the algorithm at two levels. First is the conventional FDR approach (unsupervised) at the image level. Alternatively, we propose a pixel-level supervised approach for band reduction based on time-series complexity analysis. Techniques for determining an optimal intrinsic dimension for the dataset using these two techniques are examined. We also develop a parallel GPU-based implementation for the unsupervised image-level FDR algorithm, reducing the run-time by nearly 10 times. Furthermore, both approaches use a support vector machine classifier to compare the classification performance of the original and reduced image obtained.

Nonlinear Alfvén-wave Dynamics and Premerger Emission from Crustal Oscillations in Neutron Star Mergers

Neutron stars have solid crusts threaded by strong magnetic fields. Perturbations in the crust can excite nonradial oscillations, which can in turn launch Alfvén waves into the magnetosphere. In the case of a compact binary close to merger involving at least one neutron star, this can happen through tidal interactions causing resonant excitations that shatter the neutron star crust. We present the first numerical study that elucidates the dynamics of Alfvén waves launched in a compact binary magnetosphere. We seed a magnetic field perturbation on the neutron star crust, which we then evolve in fully general-relativistic force-free electrodynamics using a GPU-based implementation. We show that Alfvén waves steepen nonlinearly before reaching the orbital light cylinder, form flares, and dissipate energy in a transient current sheet. Our results predict radio and X-ray precursor emission from this process.

GPUPRSI: GPU implementation of seismic interferometry for retrieving reflection responses from passive source seismic recordings

Passive seismic exploration is an environmentally friendly, economical, and highly accessible exploration method that is widely used in different-scale subsurface imaging. Retrieving reflections from ambient noise is a newly developed passive seismic method that can be used in many fields such as mineral exploration and near-surface imaging, but the interferometry calculation is time-consuming because it requires a longer period of data acquisition to improve the signal-to-noise ratio of the retrieved reflections. In this study, we introduced a graphical processing unit (GPU)- based implementation of seismic interferometry for retrieving reflection responses from passive source seismic recordings. Because all traces are involved in the computation process, but the size of passive source data often exceeds available memory, repeated disk reads lead to a decrease in computational efficiency. We design a strategy of grouping computations followed by stacking to minimize disk input and output, simultaneously keeping the memory requirements low. Passive source data is read and written only once, and there is no requirement for the memory size to be greater than the data size. Additionally, acceleration technologies such as asynchronous execution, asynchronous memory transfer, and GPU-accelerated libraries are used. We test the efficiency using short data where the number of sampling points per trace is on the order of 30,000, and long data, where the number of sampling points per trace is on the order of 30,000,000. For short data, the average speedup is 4 compared with a multi-core central processing unit (CPU); for long data, the speedup can reach 24. The GPU-based implementation of interferometry greatly reduces the calculation time for retrieving reflections from passive source seismic recordings, providing a solution to the problem of large calculation in three-dimensional (3D) passive source reflection exploration.

A Hybrid Monte Carlo study of argon solidification

Abstract A GPU-based implementation of the Hybrid Monte Carlo (HMC) algorithm is presented to explore its utility in the chemistry of solidification at the example of liquid to solid argon. We validate our implementation by comparing structural characteristics of argon fluid-like phases from HMC and MD simulations. Examining solidification, both MD and HMC show similar trends. Despite observable differences, MD simulations and HMC agree within the errors during the phase transition. Introducing voids decreases the solidification temperature, aiding in the formation of a well-structured solids. Further, our findings highlight the importance of larger system sizes in simulating solidification processes. Simulations with a temperature dependent potential show ambiguous results for the solidification which may be attributed to the small system sizes. Future work aims to expand HMC capabilities for complex chemical phenomena in phase transitions.

SEMG-Based Robust Recognition of Grasping Postures with a Machine Learning Approach for Low-Cost Hand Control.

The design and control of artificial hands remains a challenge in engineering. Popular prostheses are bio-mechanically simple with restricted manipulation capabilities, as advanced devices are pricy or abandoned due to their difficult communication with the hand. For social robots, the interpretation of human intention is key for their integration in daily life. This can be achieved with machine learning (ML) algorithms, which are barely used for grasping posture recognition. This work proposes an ML approach to recognize nine hand postures, representing 90% of the activities of daily living in real time using an sEMG human-robot interface (HRI). Data from 20 subjects wearing a Myo armband (8 sEMG signals) were gathered from the NinaPro DS5 and from experimental tests with the YCB Object Set, and they were used jointly in the development of a simple multi-layer perceptron in MATLAB, with a global percentage success of 73% using only two features. GPU-based implementations were run to select the best architecture, with generalization capabilities, robustness-versus-electrode shift, low memory expense, and real-time performance. This architecture enables the implementation of grasping posture recognition in low-cost devices, aimed at the development of affordable functional prostheses and HRI for social robots.

GIPC: Fast and Stable Gauss-Newton Optimization of IPC Barrier Energy

Barrier functions are crucial for maintaining an intersection- and inversion-free simulation trajectory but existing methods, which directly use distance can restrict implementation design and performance. We present an approach to rewriting the barrier function for arriving at an efficient and robust approximation of its Hessian. The key idea is to formulate a simplicial geometric measure of contact using mesh boundary elements, from which analytic eigensystems are derived and enhanced with filtering and stiffening terms that ensure robustness with respect to the convergence of a Project-Newton solver. A further advantage of our rewriting of the barrier function is that it naturally caters to the notorious case of nearly parallel edge-edge contacts for which we also present a novel analytic eigensystem. Our approach is thus well suited for standard second-order unconstrained optimization strategies for resolving contacts, minimizing nonlinear nonconvex functions where the Hessian may be indefinite. The efficiency of our eigensystems alone yields a 3× speedup over the standard Incremental Potential Contact (IPC) barrier formulation. We further apply our analytic proxy eigensystems to produce an entirely GPU-based implementation of IPC with significant further acceleration.

Load-Balanced Parallel Implementation on GPUs for Multi-Scalar Multiplication Algorithm

Multi-scalar multiplication (MSM) is an important building block in most of elliptic-curve-based zero-knowledge proof systems, such as Groth16 and PLONK. Recently, Lu et al. proposed cuZK, a new parallel MSM algorithm on GPUs. In this paper, we revisit this scheme and present a new GPU-based implementation to further improve the performance of MSM algorithm. First, we propose a novel method for mapping scalars into Pippenger’s bucket indices, largely reducing the number of buckets compared to the original Pippenger algorithm. Second, in the case that memory is sufficient, we develop a new efficient algorithm based on homogeneous coordinates in the bucket accumulation phase. Moreover, our accumulation phase is load-balanced, which means the parallel speedup ratio is almost linear growth as the number of device threads increases. Finally, we also propose a parallel layered reduction algorithm for the bucket aggregation phase, whose time complexity remains at the logarithmic level of the number of buckets. The implementation results over the BLS12-381 curve on the V100 graphics card show that our proposed algorithm achieves up to 1.998x, 1.821x and 1.818x speedup compared to cuZK at scales of 221, 222, and 223, respectively.

Acceleration of Graph Neural Network-Based Prediction Models in Chemistry via Co-Design Optimization on Intelligence Processing Units.

Atomic structure prediction and associated property calculations are the bedrock of chemical physics. Since high-fidelity ab initio modeling techniques for computing the structure and properties can be prohibitively expensive, this motivates the development of machine-learning (ML) models that make these predictions more efficiently. Training graph neural networks over large atomistic databases introduces unique computational challenges, such as the need to process millions of small graphs with variable size and support communication patterns that are distinct from learning over large graphs, such as social networks. We demonstrate a novel hardware-software codesign approach to scale up the training of atomistic graph neural networks (GNN) for structure and property prediction. First, to eliminate redundant computation and memory associated with alternative padding techniques and to improve throughput via minimizing communication, we formulate the effective coalescing of the batches of variable-size atomistic graphs as the bin packing problem and introduce a hardware-agnostic algorithm to pack these batches. In addition, we propose hardware-specific optimizations, including a planner and vectorization for the gather-scatter operations targeted for Graphcore's Intelligence Processing Unit (IPU), as well as model-specific optimizations such as merged communication collectives and optimized softplus. Putting these all together, we demonstrate the effectiveness of the proposed codesign approach by providing an implementation of a well-established atomistic GNN on the Graphcore IPUs. We evaluate the training performance on multiple atomistic graph databases with varying degrees of graph counts, sizes, and sparsity. We demonstrate that such a codesign approach can reduce the training time of atomistic GNNs and can improve their performance by up to 1.5× compared to the baseline implementation of the model on the IPUs. Additionally, we compare our IPU implementation with a Nvidia GPU-based implementation and show that our atomistic GNN implementation on the IPUs can run 1.8× faster on average compared to the execution time on the GPUs.

Graphics-processing-unit-accelerated ice flow solver for unstructured meshes using the Shallow-Shelf Approximation (FastIceFlo v1.0.1)

Abstract. Ice-sheet flow models capable of accurately projecting their future mass balance constitute tools to improve flood risk assessment and assist sea-level rise mitigation associated with enhanced ice discharge. Some processes that need to be captured, such as grounding-line migration, require high spatial resolution (under the kilometer scale). Conventional ice flow models mainly execute on central processing units (CPUs), which feature limited parallel processing capabilities and peak memory bandwidth. This may hinder model scalability and result in long run times, requiring significant computational resources. As an alternative, graphics processing units (GPUs) are ideally suited for high spatial resolution, as the calculations can be performed concurrently by thousands of threads, processing most of the computational domain simultaneously. In this study, we combine a GPU-based approach with the pseudo-transient (PT) method, an accelerated iterative and matrix-free solution strategy, and investigate its performance for finite elements and unstructured meshes with application to two-dimensional (2-D) models of real glaciers at a regional scale. For both the Jakobshavn and Pine Island glacier models, the number of nonlinear PT iterations required to converge a given number of vertices (N) scales in the order of 𝒪(N1.2) or better. We further compare the performance of the PT CUDA C implementation with a standard finite-element CPU-based implementation using the price-to-performance metric. The price of a single Tesla V100 GPU is 1.5 times that of two Intel Xeon Gold 6140 CPUs. We expect a minimum speedup of at least 1.5 times to justify the Tesla V100 GPU price to performance. Our developments result in a GPU-based implementation that achieves this goal with a speedup beyond 1.5 times. This study represents a first step toward leveraging GPU processing power, enabling more accurate polar ice discharge predictions. The insights gained will benefit efforts to diminish spatial resolution constraints at higher computing performance. The higher computing performance will allow for ensembles of ice-sheet flow simulations to be run at the continental scale and higher resolution, a previously challenging task. The advances will further enable the quantification of model sensitivity to changes in upcoming climate forcings. These findings will significantly benefit process-oriented sea-level-projection studies over the coming decades.

GPU-based molecular dynamics of fluid flows: Reaching for turbulence

Fluid dynamics is a ubiquitous problem that arises in different branches of science and industry. It is usually tackled by numerically solving continuum Navier-Stokes type equations. Molecular dynamics has been not a feasible tool to approach fluid dynamics until very recently due to its disproportional computational complexity for relevant system sizes. In this paper, we propose a new type of boundary conditions for molecular dynamics simulations of stationary fluid flows and present its possible GPU-based implementations in OpenMM and LAMMPS. We examine the performance and scalability of the proposed implementations. The benchmarking results show promising performance that makes it possible to reach turbulence in atomistic models of stationary fluid flows using modern supercomputers.

Gpu-based and streaming-enabled implementation of pre-processing flow towards enhancing optical character recognition accuracy and efficiency

Gpu-based and streaming-enabled implementation of pre-processing flow towards enhancing optical character recognition accuracy and efficiency

Optimized Implementation of Argon2 Utilizing the Graphics Processing Unit

In modern information technology systems, secure storage and transmission of personal and sensitive data are recognized as important tasks. These requirements are achieved through secure and robust encryption methods. Argon2 is an advanced cryptographic algorithm that emerged as the winner in the Password Hashing Competition (PHC), offering a concrete and secure measure. Argon2 also provides a secure mechanism against side-channel attacks and cracking attacks using parallel processing (e.g., GPU). In this paper, we analyze the existing GPU-based implementation of the Argon2 algorithm and further optimize the implementation by improving the performance of the hashing function during the computation process. The proposed method focuses on enhancing performance by distributing tasks between CPU and GPU units, reducing the data transfer cost for efficient GPU-based parallel processing. By shifting several stages from the CPU to the GPU, the data transfer cost is significantly reduced, resulting in faster processing times, particularly when handling a larger number of passwords and higher levels of parallelism. Additionally, we optimize the utilization of the GPU’s shared memory, which enhances memory access speed, especially in the computation of the hash value generation process. Furthermore, we leverage the parallel processing capabilities of the GPU to perform efficient brute-force attacks. By computing the H function on the GPU, the proposed implementation can generate initial blocks for multiple inputs in a single operation, making brute-force attacks in an efficient way. The proposed implementation outperforms existing methods, especially when processing a larger number of passwords and operating at higher levels of parallelism.

GGNN: Graph-Based GPU Nearest Neighbor Search

Approximate nearest neighbor (ANN) search in high dimensions is an integral part of several computer vision systems and gains importance in deep learning with explicit memory representations. Since PQT, FAISS, and SONG started to leverage the massive parallelism offered by GPUs, GPU-based implementations are a crucial resource for today's state-of-the-art ANN methods. While most of these methods allow for faster queries, less emphasis is devoted to accelerating the construction of the underlying index structures. In this paper, we propose a novel GPU-friendly search structure based on nearest neighbor graphs and information propagation on graphs. Our method is designed to take advantage of GPU architectures to accelerate the hierarchical construction of the index structure and for performing the query. Empirical evaluation shows that GGNN significantly surpasses the state-of-the-art CPU- and GPU-based systems in terms of build-time, accuracy and search speed.

Dynamic Mode Decomposition for Large-Scale Coherent Structure Extraction in Shear Flows.

Large-scale structures have been observed in many shear flows which are the fluid generated between two surfaces moving with different velocity. A better understanding of the physics of the structures (especially large-scale structures) in shear flows will help explain a diverse range of physical phenomena and improve our capability of modeling more complex turbulence flows. Many efforts have been made in order to capture such structures; however, conventional methods have their limitations, such as arbitrariness in parameter choice or specificity to certain setups. To address this challenge, we propose to use Multi-Resolution Dynamic Mode Decomposition (mrDMD), for large-scale structure extraction in shear flows. In particular, we show that the slow motion DMD modes are able to reveal large-scale structures in shear flows that also have slow dynamics. In most cases, we find that the slowest DMD mode and its reconstructed flow can sufficiently capture the large-scale dynamics in the shear flows, which leads to a parameter-free strategy for large-scale structure extraction. Effective visualization of the large-scale structures can then be produced with the aid of the slowest DMD mode. To speed up the computation of mrDMD, we provide a fast GPU-based implementation. We also apply our method to some non-shear flows that need not behave quasi-linearly to demonstrate the limitation of our strategy of using the slowest DMD mode. For non-shear flows, we show that multiple modes from different levels of mrDMD may be needed to sufficiently characterize the flow behavior.

GVLE: a highly optimized GPU-based implementation of variable-length encoding

GVLE: a highly optimized GPU-based implementation of variable-length encoding

TaiChi: A Hybrid Compression Format for Binary Sparse Matrix-Vector Multiplication on GPU

Binary Sparse Matrix-Vector Multiplication (SpMV) is a heavy computational kernel in weblink analysis, integer factorization, compressed sensing, spectral graph theory, and other domains. Testing several popular GPU-based SpMV implementations on 400 sparse matrices, we observed that data transfer to GPU memory accounts for a large part of the total computation time. The transfer of constant value “1”s can be easily eliminated for binary sparse matrices. However, compressing index arrays has always been a great challenge. This article proposes a new compression format TaiChi to further reduce index data copies and improve the performance of SpMV, especially for diagonally dominant binary sparse matrices. Input matrices are first partitioned into relatively dense and ultra-sparse areas. Then the dense areas are encoded inversely by marking “0”s, while the ultra-sparse area is encoded by marking “1”s. We also designed a new SpMV algorithm only using addition and subtraction for binary matrices based on our partition and encoding format. Evaluation results on real-world binary sparse matrices show that our hybrid encoding for binary matrix significantly reduces the data transfer and speeds up the kernel execution. It achieves the highest transfer and kernel execution speedups of 5.63x and 3.84x on GTX 1080 Ti, 3.39x and 3.91x on Tesla V100.

Highly-Parallel Hardwired Deep Convolutional Neural Network for 1-ms Dual-Hand Tracking

1-ms vision systems represent an extreme case of temporal development in video sensing techniques. Moreover, a 1-ms dual-hand tracking system leverages the dexterous functionality of hands and thus serves as a seamless and intuitive interface for Human-Computer Interaction. Deep CNN is promising for high tracking robustness, however, neither GPU-based nor FPGA-based implementation addresses the tracking task with ultra-high-speed. This paper proposes: (a) A paradigm to directly map a deep CNN as a hardwired circuit, so the entire network runs in parallel and high processing speed is obtained. The network is exempted from memory access since all intermediate neural values are implicitly represented in hardware states. And condensed binarization is used to reduce resource utilization; (b) Hardware design of the hardwired network on FPGA, inside which kernel-adapted convolutional trees are devised to maximize the parallelism. The speed bottleneck of the network is therefore removed by implementing convolutional layers as fine-grained pipelines with unified components; (c) FPGA-GPU hetero complementation, which utilizes an auxiliary GPU network to compensate for accuracy of the FPGA network without affecting its speed. The quick primary results on FPGA are intermittently refined using delayed but accurate hints from GPU. Implementation results show that the proposed method reaches 973fps and consumes merely 1.30ms to process on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$640\times 480$ </tex-math></inline-formula> images, while the accuracy is only 4.7% lower compared with the general method on test sequences. Video demonstrations are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://wcms.waseda.jp/em/5f9d020f136e7</uri> .

GPU-accelerated DNS of compressible turbulent flows

This paper explores strategies to transform an existing CPU-based high-performance computational fluid dynamics solver, HyPar, for compressible flow simulations on emerging exascale heterogeneous (CPU+GPU) computing platforms. The scientific motivation for developing a GPU-enhanced version of HyPar is to simulate canonical turbulent flows at the highest resolution possible on such platforms. We show that optimizing memory operations and thread blocks results in 200x speedup of computationally intensive kernels compared with a CPU core. Using multiple GPUs and CUDA-aware MPI communication, we demonstrate both strong and weak scaling of our GPU-based HyPar implementation on the NVIDIA Volta V100 GPUs. We simulate the decay of homogeneous isotropic turbulence in a triply periodic box on grids with up to 10243 points (5.3 billion degrees of freedom) and on up to 1,024 GPUs. We compare the wall times for CPU-only and CPU+GPU simulations. The results presented in the paper are obtained on the Summit and Lassen supercomputers at Oak Ridge and Lawrence Livermore National Laboratories, respectively.

Large scale K-means clustering using GPUs

The k-means algorithm is widely used for clustering, compressing, and summarizing vector data. We present a fast and memory-efficient GPU-based algorithm for exact k-means, Asynchronous Selective Batched K-means (ASB K-means). Unlike most GPU-based k-means algorithms that require loading the whole dataset onto the GPU for clustering, the amount of GPU memory required to run our algorithm can be chosen to be much smaller than the size of the whole dataset. Thus, our algorithm can cluster datasets whose size exceeds the available GPU memory. The algorithm works in a batched fashion and applies the triangle inequality in each k-means iteration to omit a data point if its membership assignment, i.e., the cluster it belongs to, remains unchanged, thus significantly reducing the number of data points that need to be transferred between the CPU’s RAM and the GPU’s global memory and enabling the algorithm to very efficiently process large datasets. Our algorithm can be substantially faster than a GPU-based implementation of standard k-means even in situations when application of the standard algorithm is feasible because the whole dataset fits into GPU memory. Experiments show that ASB K-means can run up to 15x times faster than a standard GPU-based implementation of k-means, and it also outperforms the GPU-based k-means implementation in NVIDIA’s open-source RAPIDS machine learning library on all the datasets used in our experiments.

Accelerating Real-Time Coupled Cluster Methods with Single-Precision Arithmetic and Adaptive Numerical Integration.

We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schrödinger equation places high demands on computing resources, particularly for high level theories such as coupled cluster with polynomial scaling. Similar to earlier investigations of coupled cluster properties, we demonstrate that the use of single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of 2 with no significant impact on the resulting UV/vis absorption spectrum computed via the Fourier transform of the time-dependent dipole moment. Additional speedups─of up to a factor of 14 in test simulations of water clusters─are obtained via a straightforward GPU-based implementation as compared to conventional CPU calculations. We also find that further performance optimization is accessible through sagacious selection of numerical integration algorithms, and the adaptive methods, such as the Cash-Karp integrator, provide an effective balance between computing costs and numerical stability. Finally, we demonstrate that a simple mixed-step integrator based on the conventional fourth-order Runge-Kutta approach is capable of stable propagations even for strong external fields, provided the time step is appropriately adapted to the duration of the laser pulse with only minimal computational overhead.