CUBE – Towards an Optimal Scaling of Cosmological N-body Simulations

Cheng, Shenggan; Yu, Hao-Ran; Inman, Derek; Liao, Qiucheng; Wu, Qiaoya; Lin, James

doi:10.1109/ccgrid49817.2020.00-22

Cited by 10 publications

(5 citation statements)

References 15 publications

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“…Fast Fourier transform (FFT) is essential in many scientific and engineering applications, including large-scale simulations [6], time series [30], waveform analysis [4], electronic structure calculations [15], and image processing [8]. Due to its wide range of applications, improving the performance of FFT is of great significance.…”

Section: Introductionmentioning

confidence: 99%

“…And a noticeable number of scientific applications use half-precision FFT. The gravitational wave data analysis software pyCBC [4] and the cosmological large-scale structure N-body code CUBE [6,32] use half precision to speed up the long-length FFT calculation. Medical image restoration applications [8,19] use lower precision or mixed precision to speed up the computation of batched 2D FFT.…”

Section: Introductionmentioning

confidence: 99%

“…We designed and implemented tcFFT, the first FFT library on Tensor Cores which supports batched 1D and 2D FFT in a wide range of sizes with high performance, and it is open-source at https:// github.com/given_in_the_official_version. It can outperform cuFFT in common half-precision FFT applied scenarios [4,6,8,19,32] and uses the similar interface to cuFFT. We have overcome the key challenges in implementing such a universal size supported FFT library with two major novel techniques.…”

Section: Introductionmentioning

confidence: 99%

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tcFFT: Accelerating Half-Precision FFT through Tensor Cores

Li,

Cheng,

Lin

2021

Preprint

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Fast Fourier Transform (FFT) is an essential tool in scientific and engineering computation. The increasing demand for mixed-precision FFT has made it possible to utilize half-precision floating-point (FP16) arithmetic for faster speed and energy saving. Specializing in lower precision, NVIDIA Tensor Cores can deliver extremely high computation performance. However, the fixed computation pattern makes it hard to utilize the computing power of Tensor Cores in FFT. Therefore, we developed tcFFT to accelerate FFT with Tensor Cores. Our tcFFT supports batched 1D and 2D FFT of various sizes and it exploits a set of optimizations to achieve high performance: 1) single-element manipulation on Tensor Core fragments to support special operations needed by FFT; 2) fine-grained data arrangement design to coordinate with the GPU memory access pattern. We evaluated our tcFFT and the NVIDIA cuFFT in various sizes and dimensions on NVIDIA V100 and A100 GPUs. The results show that our tcFFT can outperform cuFFT 1.29x-3.24x and 1.10x-3.03x on the two GPUs, respectively. Our tcFFT has a great potential for mixed-precision scientific applications. CCS CONCEPTS• Theory of computation → Massively parallel algorithms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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tcFFT: Accelerating Half-Precision FFT through Tensor Cores

Li,

Cheng,

Lin

2021

Preprint

Self Cite

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“…Guillet & Teyssier 2011), allows focusing the effort on a specific region of the computational domain, but requires a two-way flow of information between small and large scales. More recently, leading computational cosmology groups have been developing sophisticated schemes to leverage parallel and hybrid computing architectures (Gonnet et al 2013;Theuns et al 2015;Aubert et al 2015;Ocvirk et al 2016;Potter et al 2017;Yu et al 2018;Garrison et al 2019;Cheng et al 2020).…”

Section: Introductionmentioning

confidence: 99%

Perfectly parallel cosmological simulations using spatial comoving Lagrangian acceleration

Leclercq

Faure

Lavaux

et al. 2020

A&A

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Context. Existing cosmological simulation methods lack a high degree of parallelism due to the long-range nature of the gravitational force, which limits the size of simulations that can be run at high resolution. Aims. To solve this problem, we propose a new, perfectly parallel approach to simulate cosmic structure formation, which is based on the spatial COmoving Lagrangian Acceleration (sCOLA) framework. Methods. Building upon a hybrid analytical and numerical description of particles’ trajectories, our algorithm allows for an efficient tiling of a cosmological volume, where the dynamics within each tile is computed independently. As a consequence, the degree of parallelism is equal to the number of tiles. We optimised the accuracy of sCOLA through the use of a buffer region around tiles and of appropriate Dirichlet boundary conditions around sCOLA boxes. Results. As a result, we show that cosmological simulations at the degree of accuracy required for the analysis of the next generation of surveys can be run in drastically reduced wall-clock times and with very low memory requirements. Conclusions. The perfect scalability of our algorithm unlocks profoundly new possibilities for computing larger cosmological simulations at high resolution, taking advantage of a variety of hardware architectures.

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“…To reduce the computational cost of generating simulation samples various parallel, distributed-memory N -body solvers have been developed sometimes with GPU-acceleration (Springel 2005 ;Yu, Pen & Wang 2018, Cheng et al 2020. Relying solely on massively parallel computing to tackle next-generation observational data sets appears impractical given our time, memory, and energy resources since thousands of simulations are needed to produce sufficiently accurate cosmological parameter constraints (see for instance, Blot et al 2016 ).…”

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confidence: 99%

Bayesian control variates for optimal covariance estimation with pairs of simulations and surrogates

Chartier

Wandelt

2022

Monthly Notices of the Royal Astronomical Society

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Predictions of the mean and covariance matrix of summary statistics are critical for confronting cosmological theories with observations, not least for likelihood approximations and parameter inference. Accurate estimates require running costly N-body and hydrodynamics simulations. Approximate solvers, or surrogates, greatly reduce the computational cost but introduce biases, especially in the non-linear regime of structure growth. We propose ‘CARPool Bayes’ to solve the inference problem for both the means and covariances using a combination of simulations and surrogates. Our approach allows incorporating prior information for the mean and covariance. We derive closed-form solutions for Maximum A Posteriori covariance estimates that are efficient Bayesian shrinkage estimators, guarantee positive semi-definiteness, and can optionally leverage analytical covariance approximations. We discuss choices of the prior and propose a procedure for obtaining optimal prior hyperparameter values with a small set of test simulations. We test our method by estimating the covariances of clustering statistics of GADGET-IIIN-body simulations at redshift z = 0.5 using surrogates from a 100-1000× faster particle-mesh code. Taking the sample covariance from 15,000 simulations as the truth, and using an empirical Bayes prior with diagonal blocks, our estimator produces nearly identical Fisher matrix contours for ΛCDM parameters using only 15 simulations of the non-linear dark matter power spectrum. In this case the number of simulations is so small that the sample covariance is degenerate. We show cases where even with a naïve prior our method improves the estimate. Our framework is applicable to a wide range of cosmological problems where fast surrogates are available.

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CUBE – Towards an Optimal Scaling of Cosmological N-body Simulations

Cited by 10 publications

References 15 publications

tcFFT: Accelerating Half-Precision FFT through Tensor Cores

tcFFT: Accelerating Half-Precision FFT through Tensor Cores

Perfectly parallel cosmological simulations using spatial comoving Lagrangian acceleration

Bayesian control variates for optimal covariance estimation with pairs of simulations and surrogates

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