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Register a new userUsing hybrid GPU/CPU kernel splitting to accelerate spherical convolutions
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We present a general method for accelerating by more than an order of magnitude the convolution of pixelated functions on the sphere with a radially-symmetric kernel. Our method splits the kernel into a compact real-space component and a compact spherical harmonic space component. These components can then be convolved in parallel using an inexpensive commodity GPU and a CPU. We provide models for the computational cost of both real-space and Fourier space convolutions and an estimate for the approximation error. Using these models we can determine the optimum split that minimizes the wall clock time for the convolution while satisfying the desired error bounds. We apply this technique to the problem of simulating a cosmic microwave background (CMB) anisotropy sky map at the resolution typical of the high resolution maps produced by the Planck mission. For the main Planck CMB science channels we achieve a speedup of over a factor of ten, assuming an acceptable fractional rms error of order 1.e-5 in the power spectrum of the output map.
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How to improve the efficiency of routing procedures in CapsNets has been studied a lot. However, the efficiency of capsule convolutions has largely been neglected. Capsule convolution, which uses capsules rather than neurons as the basic computation unit, makes it incompatible with current deep learning frameworks optimization solution. As a result, capsule convolutions are usually very slow with these frameworks. We observe that capsule convolutions can be considered as the operations of `multiplication of multiple small matrics plus tensor-based combination. Based on this observation, we develop two acceleration schemes with CUDA APIs and test them on a custom CapsNet. The result shows that our solution achieves a 4X acceleration.
The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization potential and feasibility of peta-scale heterogeneous CPU-GPU implementations of the KPM. At the node level we show that it is possible to decouple the sparse matrix problem posed by KPM from main memory bandwidth both on CPU and GPU. To alleviate the effects of scattered data access we combine loosely coupled outer iterations with tightly coupled block sparse matrix multiple vector operations, which enables pure data streaming. All optimizations are guided by a performance analysis and modelling process that indicates how the computational bottlenecks change with each optimization step. Finally we use the optimized node-level KPM with a hybrid-parallel framework to perform large scale heterogeneous electronic structure calculations for novel topological materials on a petascale-class Cray XC30 system.
The special computational challenges of simulating 3-D hydrodynamics in deep stellar interiors are discussed, and numerical algorithmic responses described. Results of recent simulations carried out at scale on the NSFs Blue Waters machine at the University of Illinois are presented, with a special focus on the computational challenges they address. Prospects for future work using GPU-accelerated nodes such as those on the DoEs new Summit machine at Oak Ridge National Laboratory are described, with a focus on numerical algorithmic accommodations that we believe will be necessary.
In this paper we focus on the integration of high-performance numerical libraries in ab initio codes and the portability of performance and scalability. The target of our work is FLEUR, a software for electronic structure calculations developed in the Forschungszentrum Julich over the course of two decades. The presented work follows up on a previous effort to modernize legacy code by re-engineering and rewriting it in terms of highly optimized libraries. We illustrate how this initial effort to get efficient and portable shared-memory code enables fast porting of the code to emerging heterogeneous architectures. More specifically, we port the code to nodes equipped with multiple GPUs. We divide our study in two parts. First, we show considerable speedups attained by minor and relatively straightforward code changes to off-load parts of the computation to the GPUs. Then, we identify further possible improvements to achieve even higher performance and scalability. On a system consisting of 16-cores and 2 GPUs, we observe speedups of up to 5x with respect to our optimized shared-memory code, which in turn means between 7.5x and 12.5x speedup with respect to the original FLEUR code.
Moores Law and Dennard Scaling have guided the semiconductor industry for the past few decades. Recently, both laws have faced validity challenges as transistor sizes approach the practical limits of physics. We are interested in testing the validity of these laws and reflect on the reasons responsible. In this work, we collect data of more than 4000 publicly-available CPU and GPU products. We find that transistor scaling remains critical in keeping the laws valid. However, architectural solutions have become increasingly important and will play a larger role in the future. We observe that GPUs consistently deliver higher performance than CPUs. GPU performance continues to rise because of increases in GPU frequency, improvements in the thermal design power (TDP), and growth in die size. But we also see the ratio of GPU to CPU performance moving closer to parity, thanks to new SIMD extensions on CPUs and increased CPU core counts.
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