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Register a new userA Hybrid MPI-CUDA Approach for Nonequispaced Discrete Fourier Transformation
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Nonequispaced discrete Fourier transformation (NDFT) is widely applied in all aspects of computational science and engineering. The computational efficiency and accuracy of NDFT has always been a critical issue in hindering its comprehensive applications both in intensive and in extensive aspects of scientific computing. In our previous work (2018, S.-C. Yang et al., Appl. Comput. Harmon. Anal. 44, 273), a CUNFFT method was proposed and it shown outstanding performance in handling NDFT at intermediate scale based on CUDA (Compute Unified Device Architecture) technology. In the current work, we further improved the computational efficiency of the CUNTTF method using an efficient MPI-CUDA hybrid parallelization (HP) scheme of NFFT to achieve a cutting-edge treatment of NDFT at super extended scale. Within this HP-NFFT method, the spatial domain of NDFT is decomposed into several parts according to the accumulative feature of NDFT and the detailed number of CPU and GPU nodes. These decomposed NDFT subcells are independently calculated on different CPU nodes using a MPI process-level parallelization mode, and on different GPU nodes using a CUDA threadlevel parallelization mode and CUNFFT algorithm. A massive benchmarking of the HP-NFFT method indicates that this method exhibit a dramatic improvement in computational efficiency for handling NDFT at super extended scale without loss of computational precision. Furthermore, the HP-NFFT method is validated via the calculation of Madelung constant of fluorite crystal structure, and thereafter verified that this method is robust for the calculation of electrostatic interactions between charged ions in molecular dynamics simulation systems.
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In this work, we present two parallel algorithms for the large-scale discrete Fourier transform (DFT) on Tensor Processing Unit (TPU) clusters. The two parallel algorithms are associated with two formulations of DFT: one is based on the Kronecker product, to be specific, dense matrix multiplications between the input data and the Vandermonde matrix, denoted as KDFT in this work; the other is based on the famous Cooley-Tukey algorithm and phase adjustment, denoted as FFT in this work. Both KDFT and FFT formulations take full advantage of TPUs strength in matrix multiplications. The KDFT formulation allows direct use of nonuniform inputs without additional step. In the two parallel algorithms, the same strategy of data decomposition is applied to the input data. Through the data decomposition, the dense matrix multiplications in KDFT and FFT are kept local within TPU cores, which can be performed completely in parallel. The communication among TPU cores is achieved through the one-shuffle scheme in both parallel algorithms, with which sending and receiving data takes place simultaneously between two neighboring cores and along the same direction on the interconnect network. The one-shuffle scheme is designed for the interconnect topology of TPU clusters, minimizing the time required by the communication among TPU cores. Both KDFT and FFT are implemented in TensorFlow. The three-dimensional complex DFT is performed on an example of dimension $8192 times 8192 times 8192$ with a full TPU Pod: the run time of KDFT is 12.66 seconds and that of FFT is 8.3 seconds. Scaling analysis is provided to demonstrate the high parallel efficiency of the two DFT implementations on TPUs.
With AMD reinforcing their ambition in the scientific high performance computing ecosystem, we extend the hardware scope of the Ginkgo linear algebra package to feature a HIP backend for AMD GPUs. In this paper, we report and discuss the porting effort from CUDA, the extension of the HIP framework to add missing features such as cooperative groups, the performance price of compiling HIP code for AMD architectures, and the design of a library providing native backends for NVIDIA and AMD GPUs while minimizing code duplication by using a shared code base.
Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be trusted to write good code. In this manuscript we describe ModelingToolkit (MTK), a symbolic equation-based modeling system which allows for composable transformations to generate stable, efficient, and parallelized model implementations. MTK blurs the lines of traditional symbolic computing by acting directly on a users numerical code. We show the ability to apply graph algorithms for automatically parallelizing and performing index reduction on code written for differential-algebraic equation (DAE) solvers, fixing the performance and stability of the model without requiring any changes to on the users part. We demonstrate how composable model transformations can be combined with automated data-driven surrogate generation techniques, allowing machine learning methods to generate accelerated approximate models within an acausal modeling framework. These reduced models are shown to outperform the Dymola Modelica compiler on an HVAC model by 590x at 3% error. Together, this demonstrates MTK as a system for bringing the latest research in graph transformations directly to modeling applications.
Our goal is compression of massive-scale grid-structured data, such as the multi-terabyte output of a high-fidelity computational simulation. For such data sets, we have developed a new software package called TuckerMPI, a parallel C++/MPI software package for compressing distributed data. The approach is based on treating the data as a tensor, i.e., a multidimensional array, and computing its truncated Tucker decomposition, a higher-order analogue to the truncated singular value decomposition of a matrix. The result is a low-rank approximation of the original tensor-structured data. Compression efficiency is achieved by detecting latent global structure within the data, which we contrast to most compression methods that are focused on local structure. In this work, we describe TuckerMPI, our implementation of the truncated Tucker decomposition, including details of the data distribution and in-memory layouts, the parallel and serial implementations of the key kernels, and analysis of the storage, communication, and computational costs. We test the software on 4.5 terabyte and 6.7 terabyte data sets distributed across 100s of nodes (1000s of MPI processes), achieving compression rates between 100-200,000$times$ which equates to 99-99.999% compression (depending on the desired accuracy) in substantially less time than it would take to even read the same dataset from a parallel filesystem. Moreover, we show that our method also allows for reconstruction of partial or down-sampled data on a single node, without a parallel computer so long as the reconstructed portion is small enough to fit on a single machine, e.g., in the instance of reconstructing/visualizing a single down-sampled time step or computing summary statistics.
MPI derived datatypes are an abstraction that simplifies handling of non-contiguous data in MPI applications. These datatypes are recursively constructed at runtime from primitive Named Types defined in the MPI standard. More recently, the development and deployment of CUDA-aware MPI implementations has encouraged the transition of distributed high-performance MPI codes to use GPUs. Such implementations allow MPI functions to directly operate on GPU buffers, easing integration of GPU compute into MPI codes. This work first presents a novel datatype handling strategy for nested strided datatypes, which finds a middle ground between the specialized or generic handling in prior work. This work also shows that the performance characteristics of non-contiguous data handling can be modeled with empirical system measurements, and used to transparently improve MPI_Send/Recv latency. Finally, despite substantial attention to non-contiguous GPU data and CUDA-aware MPI implementations, good performance cannot be taken for granted. This work demonstrates its contributions through an MPI interposer library, TEMPI. TEMPI can be used with existing MPI deployments without system or application changes. Ultimately, the interposed-library model of this work demonstrates MPI_Pack speedup of up to 242000x and MPI_Send speedup of up to 59000x compared to the MPI implementation deployed on a leadership-class supercomputer. This yields speedup of more than 917x in a 3D halo exchange with 3072 processes.
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