Graphics Processing Unit Version Research Articles

Matrix‐based implementation and GPU acceleration of hybrid FEM and peridynamic model for hydro‐mechanical coupled problems

AbstractThe hybrid finite element‐peridynamic (FEM‐PD) models have been evidenced for their exceptional ability to address hydro‐mechanical coupled problems involving cracks. Nevertheless, the non‐local characteristics of the PD equations and the required inversion operations when solving fluid equations result in prohibitively high computational costs. In this paper, a fast explicit solution scheme for FEM‐PD models based on matrix operation is introduced, where the graphics processing units (GPUs) are used to accelerate the computation. An in‐house software is developed in MATLAB in both CPU and GPU versions. We first solve a problem related to pore pressure distribution in a single crack, demonstrating the accuracy of the proposed method by a comparison of FEM‐PD solutions with those of PD‐only models and analytical solutions. Subsequently, several examples are solved, including a one‐dimensional dynamic consolidation problem and the fluid‐driven hydraulic fracture propagation problems in both 2D and 3D cases, to comprehensively validate the effectiveness of the proposed methods in simulating deformation and fracture in saturated porous media under the influence of hydro‐mechanical coupling. In the presented numerical results, some typical strong dynamic phenomena, such as stepwise crack advancement, crack branching, and pressure oscillations, are observed. In addition, we compare the wall times of all the cases executed on both the GPU and CPU, highlighting the substantial acceleration performance of the GPU, particularly when tackling problems with a significant computational workload.

New strategies for developing GPU accelerated disk‐based discontinuous deformation analysis for large‐scale modeling

AbstractThe major obstacle for the application of discontinuous deformation analysis (DDA) in engineering problems is the high computational cost and poor efficiency. In this paper, the main algorithms of disk‐based DDA are redesigned and implemented on graphics processing unit (GPU) to improve its performance. First, a contact pair‐wise scheme is proposed to assemble the stiffness matrix on GPU. Second, a buffer strategy and a GPU version of grid‐based contact detection algorithm are developed to improve the efficiency of contact detection. Third, for solving the simultaneous equations, two iterative methods are considered along with the direct solver method. The parallel performances of proposed strategies are tested and compared with the CPU counterparts. The results show that the maximum speedup ratio is 14 for the assembly of the stiffness matrix and 215 for contact detection. The speedup ratio for solving simultaneous equations depends on several factors, and the preconditioned conjugate gradients method (pcg) is suggested. Finally, the effectiveness and performance of the proposed GPU accelerated disk‐based DDA is further demonstrated by several examples, one of which consisted of over 500,000 particles. The results show that the proposed method can achieve a satisfactory speedup ratio, and is ready for large‐scale problems.

GPU‐accelerated and mixed norm regularized online extreme learning machine

SummaryExtreme learning machine (ELM) is a prominent example of neural network with its fast training speed, and good prediction performance. An online version of ELM called online sequential extreme learning machine (OS‐ELM) has also been proposed for the sequential training. Combined with the need for regularization to prevent over‐fitting in addition to the large number of neurons required in the hidden layer, OS‐ELM demands huge amount of computation power for the large‐scale data. In this article, a mixed norm () regularized online machine learning algorithm (MRO‐ELM) that is based on alternating direction method of multipliers (ADMM) is proposed. A linear combination of the mixed norm and the Frobenius norm regularization is applied using the ADMM framework and update formulas are derived. Graphics processing unit (GPU) accelerated version of MRO‐ELM (GPU‐MRO‐ELM) is also proposed to reduce the training time by processing appropriate parts in parallel using the implemented custom kernels. In addition, a novel automatic hyper‐parameter tuning method is incorporated to GPU‐MRO‐ELM using progressive validation with GPU acceleration. The experimental results show that the MRO‐ELM algorithm and its GPU version outperform OS‐ELM in terms of training speed, and testing accuracy. Also, compared to the cross validation, the proposed automatic hyper‐parameter tuning demonstrates dramatical reduction in the tuning time.

A GPU-Accelerated and LTS-Based Finite Volume Shallow Water Model

This paper presents a GPU (Graphics Processing Unit)-accelerated and LTS (Local-time-Step)-based finite volume Shallow Water Model (SWM). The model performance is compared against the other five model versions (Single CPU versions with/without LTS, Multi-CPU versions with/without LTS, and a GPU version) by simulating three flow scenarios: an idealized dam-break flow; an experimental dam-break flow; a field-scale scenario of tidal flows. Satisfactory agreements between simulation results and the available measured data/reference solutions (water level, flow velocity) indicate that all the six SWM versions can well simulate these challenging shallow water flows. Inter-comparisons of the computational efficiency of the six SWM versions indicate the following. First, GPU acceleration is much more efficient than multi-core CPU parallel computing. Specifically, the speed increase in the GPU can be as high as a hundred, whereas those for multi-core CPU are only 2–3. Second, implementing the LTS can bring considerable reduction: the additional maximum speed-ups can be as high as 10 for the single-core CPU/multi-core CPU versions, and as high as five for the GPU versions. Third, the GPU + LTS version is computationally the most efficient in most cases; the multi-core CPU + LTS version may run as fast as a GPU version for scenarios over some intermediate number of cells.

A GPU-accelerated particle-detection algorithm for real-time volumetric particle-tracking velocimetry under non-uniform illumination

Real-time volumetric particle tracking velocimetry (VPTV) equipped with field-programmable gate array (FPGA) cameras has been used for open-space, low particle density, and large-scale airflow measurements with long measurement periods. However, the particle detection accuracy of FPGA cameras is inevitably hindered by non-uniform illumination, resulting in a reduction in the particle detection ratio and positional accuracy. In this article, we propose to use both synchronized FPGA and grayscale cameras in a VPTV system, where grayscale cameras utilize a new algorithm based on two-frame centroid and corner extraction (TFCCE) under non-uniform white-light illumination. To keep the frame rate of the FPGA cameras the same, the TFCCE algorithm was accelerated by a graphics processing unit (GPU). The simulation results showed that the 2D particle detection ratio of TFCCE was enhanced to approximately 80% with a positional accuracy of 0.57 pixels, compared to 30% and 0.94 pixels for the single-frame centroid extraction used in the FPGA. The GPU version of TFCCE was 15.09 times faster than the CPU version, resulting in a calculation time of 4.55 ms per image, compared to 68.70 ms when using the CPU. This system was also validated by the measurement of a turbulent jet flow in real-time at 120 fps. The experimental results correspond well with data published in the literature. Therefore, this new algorithm can improve VPTV systems in terms of particle detection ratio and positional accuracy in real time under conditions of non-uniform illumination.

The GPU version of LASG/IAP Climate System Ocean Model version 3 (LICOM3) under the heterogeneous-compute interface for portability (HIP) framework and its large-scale application

Abstract. A high-resolution (1/20∘) global ocean general circulation model with graphics processing unit (GPU) code implementations is developed based on the LASG/IAP Climate System Ocean Model version 3 (LICOM3) under a heterogeneous-compute interface for portability (HIP) framework. The dynamic core and physics package of LICOM3 are both ported to the GPU, and three-dimensional parallelization (also partitioned in the vertical direction) is applied. The HIP version of LICOM3 (LICOM3-HIP) is 42 times faster than the same number of CPU cores when 384 AMD GPUs and CPU cores are used. LICOM3-HIP has excellent scalability; it can still obtain a speedup of more than 4 on 9216 GPUs compared to 384 GPUs. In this phase, we successfully performed a test of 1/20∘ LICOM3-HIP using 6550 nodes and 26 200 GPUs, and on a large scale, the model's speed was increased to approximately 2.72 simulated years per day (SYPD). By putting almost all the computation processes inside GPUs, the time cost of data transfer between CPUs and GPUs was reduced, resulting in high performance. Simultaneously, a 14-year spin-up integration following phase 2 of the Ocean Model Intercomparison Project (OMIP-2) protocol of surface forcing was performed, and preliminary results were evaluated. We found that the model results had little difference from the CPU version. Further comparison with observations and lower-resolution LICOM3 results suggests that the 1/20∘ LICOM3-HIP can reproduce the observations and produce many smaller-scale activities, such as submesoscale eddies and frontal-scale structures.

GPU-RRTMG_SW: Accelerating a Shortwave Radiative Transfer Scheme on GPU

As high performance computing technology continues to develop rapidly, graphics processing units (GPUs) are more widely used for daily computing tasks. However, some applications, such as weather forecasting, require large-scale computation. Thus, due to the computationally intensive characteristics of the rapid radiative transfer model for general circulation models (RRTMG) in the Earth system model, this study uses GPU-related technology to accelerate computation of the model. First, two kinds of algorithms using GPU technology to accelerate the RRTMG shortwave radiation scheme (RRTMG_SW) are proposed. Then, an optimization method for data transmission between host and device is proposed. Finally, after using CUDA Fortran and CUDA C to implement these algorithms, two GPU versions of RRTMG_SW, namely CF-RRTMG_SW (CUDA Fortran version) and CC-RRTMG_SW (CUDA C version), were developed. The experimental results demonstrate that the proposed acceleration algorithms are effective. Without I/O transfer, running CC-RRTMG_SW on a NVIDIA GeForce Titan V GPU achieved a 38.88× speedup when compared to a single Intel Xeon E5-2680 CPU core.

Using a GPU to Accelerate a Longwave Radiative Transfer Model with Efficient CUDA-Based Methods

Climatic simulations rely heavily on high-performance computing. As one of the atmospheric radiative transfer models, the rapid radiative transfer model for general circulation models (RRTMG) is used to calculate the radiative transfer of electromagnetic radiation through a planetary atmosphere. Radiation physics is one of the most time-consuming physical processes, so the RRTMG presents large-scale and long-term simulation challenges to the development of efficient parallel algorithms that fit well into multicore clusters. This paper presents a method for improving the calculative efficiency of radiation physics, an RRTMG long-wave radiation scheme (RRTMG_LW) that is accelerated on a graphics processing unit (GPU). First, a GPU-based acceleration algorithm with one-dimensional domain decomposition is proposed. Then, a second acceleration algorithm with two-dimensional domain decomposition is presented. After the two algorithms were implemented in Compute Unified Device Architecture (CUDA) Fortran, a GPU version of the RRTMG_LW, namely G-RRTMG_LW, was developed. Results demonstrated that the proposed acceleration algorithms were effective and that the G-RRTMG_LW achieved a significant speedup. In the case without I/O transfer, the 2-D G-RRTMG_LW on one K40 GPU obtained a speed increase of 18.52× over the baseline performance on a single Intel Xeon E5-2680 CPU core.

Using GPU to accelerate the pairwise structural RNA alignment with base pair probabilities

SummaryStructural alignments of Ribonucleic acid (RNA) sequences solved by the Sankoff algorithm are computationally expensive and often require constraints to be used in practice. Modern Graphics Processing Units (GPUs) contain more than 1000 cores, which compute in parallel to speed up applications. Here, we present a GPU‐based solution to the RNA structural alignment problem that makes use of precalculated base pair probabilities on the individual sequences. We designed and developed an unconstrained version of the Sankoff algorithm, obtaining the optimal result and calculating the entire four‐dimension dynamic programming matrix (4D DP). Our approach uses a two‐level wavefront strategy to exploit parallelism. The 4D DP matrix is divided in one external matrix (EM) and several internal matrices (IM). We applied wavefront strategies on the EM and IMs in a two‐level hierarchical way. At the first level, the wavefront is applied to the EM, calculating the cells that belong to the same diagonal in parallel. In the second level, since each cell in the EM is itself an IM matrix, the cells that belong to the same IM diagonal are calculated in parallel. The results obtained with real RNA sequences show that our GPU version is capable of outperforming a multicore CPU version of the unconstrained version of the Sankoff algorithm. Compared with the CPU‐based version running on 32 cores, our approach is able to achieve a speedup of 7.81x on the NVidia Tesla P100. In this case, the execution time was reduced from 6 hours and 18 minutes (32 cores) to 48 minutes and 20 seconds (GPU).

ASTRAL-MP: scaling ASTRAL to very large datasets using randomization and parallelization.

Evolutionary histories can change from one part of the genome to another. The potential for discordance between the gene trees has motivated the development of summary methods that reconstruct a species tree from an input collection of gene trees. ASTRAL is a widely used summary method and has been able to scale to relatively large datasets. However, the size of genomic datasets is quickly growing. Despite its relative efficiency, the current single-threaded implementation of ASTRAL is falling behind the data growth trends is not able to analyze the largest available datasets in a reasonable time. ASTRAL uses dynamic programing and is not trivially parallel. In this paper, we introduce ASTRAL-MP, the first version of ASTRAL that can exploit parallelism and also uses randomization techniques to speed up some of its steps. Importantly, ASTRAL-MP can take advantage of not just multiple CPU cores but also one or several graphics processing units (GPUs). The ASTRAL-MP code scales very well with increasing CPU cores, and its GPU version, implemented in OpenCL, can have up to 158× speedups compared to ASTRAL-III. Using GPUs and multiple cores, ASTRAL-MP is able to analyze datasets with 10000 species or datasets with more than 100000 genes in <2 days. ASTRAL-MP is available at https://github.com/smirarab/ASTRAL/tree/MP. Supplementary data are available at Bioinformatics online.

Accelerating the task/data-parallel version of ILUPACK’s BiCG in multi-CPU/GPU configurations

ILUPACK is a valuable tool for the solution of sparse linear systems via iterative Krylov subspace-based methods. Its relevance for the solution of real problems has motivated several efforts to enhance its performance on parallel machines. In this work we focus on exploiting the task-level parallelism derived from the structure of the BiCG method, in addition to the data-level parallelism of the internal matrix computations, with the goal of boosting the performance of a GPU (graphics processing unit) implementation of this solver. First, we revisit the use of dual-GPU systems to execute independent stages of the BiCG concurrently on both accelerators, while leveraging the extra memory space to improve the data access patterns. In addition, we extend our ideas to compute the BiCG method efficiently in multicore platforms with a single GPU. In this line, we study the possibilities offered by hybrid CPU-GPU computations, as well as a novel synchronization-free sparse triangular linear solver. The experimental results with the new solvers show important acceleration factors with respect to the previous data-parallel CPU and GPU versions.

GPU acceleration and performance of the particle-beam-dynamics code Elegant

Elegant is an accelerator physics and particle-beam dynamics code widely used for modeling and design of a variety of high-energy particle accelerators and accelerator-based systems. In this paper we discuss a recently developed version of the code that can take advantage of CUDA-enabled graphics processing units (GPUs) to achieve significantly improved performance for a large class of simulations that are important in practice. The GPU version is largely defined by a framework that simplifies implementations of the fundamental kernel types that are used by Elegant: particle operations, reductions, particle loss, histograms, array convolutions and random number generation. Accelerated performance on the Titan Cray XK-7 supercomputer is approximately 6–10 times better with the GPU than all the CPU cores associated with the same node count. In addition to performance, the maintainability of the GPU-accelerated version of the code was considered a key design objective. Accuracy with respect to the CPU implementation is also a core consideration. Four different methods are used to ensure that the accelerated code faithfully reproduces the CPU results. Program summaryProgram Title: Kernels from the GPU-accelerated ElegantProgram Files doi:http://dx.doi.org/10.17632/jc465zy7p5.1Licensing provisions: MITProgramming language: C/C++/CUDANature of problem: The original design of the Elegant accelerator physics code was implemented on central processing units with message-passing interface parallelization. This implementation is not able to use next-generation multicore systems.Solution method: In this package we develop routines based on the CUDA language extensions to C++ that enable porting the Elegant code to be run on graphics processing units (GPUs). Special consideration is given to algorithms that require collective communication on the GPU.Additional comments including restrictions and unusual features: The full Elegant source code is freely available from Argonne National Laboratory and these distributions include the GPU code in the later releases.

Improved MPS method and its variations for simulating incompressible fluids on GPU

Meshless methods to simulate fluid flows have been increasingly evolving through the years since they are a great alternative to deal with large deformations, which is where meshbased methods fail to perform efficiently. A well known meshless method is the Moving Particle Semi-implicit (MPS) method, which was designed to simulate free-surface truly incompressible fluid flows. Many variations and refinements of the method’s accuracy and precision have been proposed through the years and, in this paper, a reasonably wide literature review was performed together with their theoretical and mathematical explanations. Due to these works, it has proved to be very useful in a wide range of naval and mechanical engineering problems. However, one of its drawbacks is a high computational load and some quite time-consuming functions, which prevents it to be more used in Computer Graphics and Virtual Reality applications. Graphics Processing Units (GPU) provide unprecedented capabilities for scientific computations. To promote the GPU-acceleration, the solution of the Poisson Pressure equation was brought into focus. This work benefits from some of the techniques presented in the related work and also from the CUDA language in order to get a stable, accurate and GPU-accelerated MPS-based method, which is this work’s main contribution. It is shown that the GPU version of the method developed can perform from, approximately, 6 to 10 times faster with the same reliability as the CPU version, both extended to three dimensions. Lastly, a simulation containing a total of 62,600 particles is fully rendered in 3D.

Computational Benefit of GPU Optimization for the Atmospheric Chemistry Modeling

AbstractGlobal chemistry‐climate models are computationally burdened as the chemical mechanisms become more complex and realistic. Optimization for graphics processing units (GPU) may make longer global simulation with regional detail possible, but limited study has been done to explore the potential benefit for the atmospheric chemistry modeling. Hence, in this study, the second‐order Rosenbrock solver of the chemistry module of CAM4‐Chem is ported to the GPU to gauge potential speed‐up. We find that on the CPU, the fastest performance is achieved using the Intel compiler with a block interleaved memory layout. Different combinations of compiler and memory layout lead to ~11.02× difference in the computational time. In contrast, the GPU version performs the best when using a combination of fully interleaved memory layout with block size equal to the warp size, CUDA streams for independent kernels, and constant memory. Moreover, the most efficient data transfer between CPU and GPU is gained by allocating the memory contiguously during the data initialization on the GPU. Compared to one CPU core, the speed‐up of using one GPU alone reaches a factor of ~11.7× for the computation alone and ~3.82× when the data transfer between CPU and GPU is considered. Using one GPU alone is also generally faster than the multithreaded implementation for 16 CPU cores in a compute node and the single‐source solution (OpenACC). The best performance is achieved by the implementation of the hybrid CPU/GPU version, but rescheduling the workload among the CPU cores is required before the practical CAM4‐Chem simulation.

Parallel cloth simulation with GPGPU

In a 3D simulation, numerous physically and numerically related calculations are required to represent an object realistically. The existing CPU (central processing unit) technology, however, is incapable of handling such a large computational amount in real time. With the recent hardware-technology advancements, the GPU (graphics processing unit) can be used not only for conventional rendering operations, but also for general-purpose computational functions. In this paper, a mass-spring system for which the CPU and GPU versions are tested under the PC and mobile environments wherein the GPGPU (general-purpose computing on GPUs) is applied is proposed. For this paper, a virtual cloth with a mass-spring system was freely dropped onto a table, and the CPU and GPU performances were compared. The computational GPU performances regarding the PC and mobile devices were improved by 9.41 times and 45.11 times, respectively, compared with the CPU. The proposed GPU mass-spring system was then implemented with an edge-centric algorithm and a node-centric algorithm. The edge-centric algorithm is divided into two parts as follows: one for the spring-force calculation and one for the node-position calculation. These two parts are combined into a single computational process for the node-centric algorithm. For this paper, the computational speeds of the two algorithms were measured. The node-centric algorithm is faster than the edge-centric algorithm under the PC environment, but the edge-centric algorithm is faster under the mobile environment.

A GPU-based symmetric non-rigid image registration method in human lung.

Quantitative computed tomography (QCT) of the lungs plays an increasing role in identifying sub-phenotypes of pathologies previously lumped into broad categories such as chronic obstructive pulmonary disease and asthma. Methods for image matching and linking multiple lung volumes have proven useful in linking structure to function and in the identification of regional longitudinal changes. Here, we seek to improve the accuracy of image matching via the use of a symmetric multi-level non-rigid registration employing an inverse consistent (IC) transformation whereby images are registered both in the forward and reverse directions. To develop the symmetric method, two similarity measures, the sum of squared intensity difference (SSD) and the sum of squared tissue volume difference (SSTVD), were used. The method is based on a novel generic mathematical framework to include forward and backward transformations, simultaneously, eliminating the need to compute the inverse transformation. Two implementations were used to assess the proposed method: a two-dimensional (2-D) implementation using synthetic examples with SSD, and a multi-core CPU and graphics processing unit (GPU) implementation with SSTVD for three-dimensional (3-D) human lung datasets (six normal adults studied at total lung capacity (TLC) and functional residual capacity (FRC)). Success was evaluated in terms of the IC transformation consistency serving to link TLC to FRC. 2-D registration on synthetic images, using both symmetric and non-symmetric SSD methods, and comparison of displacement fields showed that the symmetric method gave a symmetrical grid shape and reduced IC errors, with the mean values of IC errors decreased by 37%. Results for both symmetric and non-symmetric transformations of human datasets showed that the symmetric method gave better results for IC errors in all cases, with mean values of IC errors for the symmetric method lower than the non-symmetric methods using both SSD and SSTVD. The GPU version demonstrated an average of 43 times speedup and ~5.2 times speedup over the single-threaded and 12-threaded CPU versions, respectively. Run times with the GPU were as fast as 2min. The symmetric method improved the inverse consistency, aiding the use of image registration in the QCT-based evaluation of the lung.

Exploring hidden coherency of Ray-Tracing for heterogeneous systems using online feedback methodology

Although naturally adopting an embarrassingly parallel paradigm, Ray-Tracing is also categorized as an irregular program that is troublesome to run on graphics processing units (GPUs). Conventional designs suffer from a performance penalty due to the irregularity of the control flow and memory access caused by incoherent rays. This work aims to explore the hidden coherency of rays by designing a feedback-guided mechanism that serves the following concept: extraction of the hidden regular portions out of the irregular execution flow. The method records the correlation of ray attributes and the traversed path and groups the newly generated rays to reduce potential irregularities for the ongoing execution. This mechanism captures the information from the entire ray space and can extract the hidden coherency from both primary and derived rays. The result leads to performance gains and an increase in resource utilization. The performance becomes 2 to 2.5 times higher than the original GPU and CPU versions.

Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM

This paper presents the parallel computing implementation of the MitISEM algorithm, labeled Parallel MitISEM. The basic MitISEM algorithm provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. We present and discuss four canonical econometric models using a Graphics Processing Unit and a multi-core Central Processing Unit version of the MitISEM algorithm. The results show that the parallelization of the MitISEM algorithm on Graphics Processing Units and multi-core Central Processing Units is straightforward and fast to program using MATLAB. Moreover the speed performance of the Graphics Processing Unit version is much higher than the Central Processing Unit one.

Efficient methods for implementation of multi-level nonrigid mass-preserving image registration on GPUs and multi-threaded CPUs

Background and objectiveFaster and more accurate methods for registration of images are important for research involved in conducting population-based studies that utilize medical imaging, as well as improvements for use in clinical applications. We present a novel computation- and memory-efficient multi-level method on graphics processing units (GPU) for performing registration of two computed tomography (CT) volumetric lung images. MethodsWe developed a computation- and memory-efficient Diffeomorphic Multi-level B-Spline Transform Composite (DMTC) method to implement nonrigid mass-preserving registration of two CT lung images on GPU. The framework consists of a hierarchy of B-Spline control grids of increasing resolution. A similarity criterion known as the sum of squared tissue volume difference (SSTVD) was adopted to preserve lung tissue mass. The use of SSTVD consists of the calculation of the tissue volume, the Jacobian, and their derivatives, which makes its implementation on GPU challenging due to memory constraints. The use of the DMTC method enabled reduced computation and memory storage of variables with minimal communication between GPU and Central Processing Unit (CPU) due to ability to pre-compute values. The method was assessed on six healthy human subjects. ResultsResultant GPU-generated displacement fields were compared against the previously validated CPU counterpart fields, showing good agreement with an average normalized root mean square error (nRMS) of 0.044±0.015. Runtime and performance speedup are compared between single-threaded CPU, multi-threaded CPU, and GPU algorithms. Best performance speedup occurs at the highest resolution in the GPU implementation for the SSTVD cost and cost gradient computations, with a speedup of 112 times that of the single-threaded CPU version and 11 times over the twelve-threaded version when considering average time per iteration using a Nvidia Tesla K20X GPU. ConclusionsThe proposed GPU-based DMTC method outperforms its multi-threaded CPU version in terms of runtime. Total registration time reduced runtime to 2.9min on the GPU version, compared to 12.8min on twelve-threaded CPU version and 112.5min on a single-threaded CPU. Furthermore, the GPU implementation discussed in this work can be adapted for use of other cost functions that require calculation of the first derivatives.

Accelerating viability kernel computation with CUDA architecture: application to bycatch fishery management

Computing a viability kernel consumes time and memory resources which increase exponentially with the dimension of the problem. This curse of dimensionality strongly limits the applicability of this approach, otherwise promising. We report here an attempt to tackle this problem with Graphics Processing Units (GPU). We design and implement a version of the viability kernel algorithm suitable for General Purpose GPU (GPGPU) computing using Nvidia’s architecture, CUDA (Computing Unified Device Architecture). Different parts of the algorithm are parallelized on the GPU device and we test the algorithm on a dynamical system of theoretical population growth. We study computing time gains as a function of the number of dimensions and the accuracy of the grid covering the state space. The speed factor reaches up to 20 with the GPU version compared to the Central Processing Unit (CPU) version, making the approach more applicable to problems in 4 to 7 dimensions. We use the GPU version of the algorithm to compute viability kernel of bycatch fishery management problems up to 6 dimensions.