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Results for “mixed-precision arithmetic”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network

In this work, time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix–matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree–Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

High-Performance GMRES Mixed-Precision (HPG-MxP) Benchmark

SAND2024-08539O The High Performance GMRES Mixed-Precision (HPG-MxP) is a benchmark for ranking high-performance supercomputers, allowing use of mixed-precision. Similar to HPCG benchmark, it is designed to profile the computers' capabilities to perform the computational and communication tasks that are commonly found in important classes of real-world applications. At the same time, like HPL-MxP benchmark, it allows the use of mixed-precision arithmetic, while ensuring the double-precision accuracy of the computed solution. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2022

DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization

In this work, we present DFT-FE 1.0, building on DFT-FE 0.6 [Comput. Phys. Commun. 246, 106853 (2020)], to conduct fast and accurate large-scale density functional theory (DFT) calculations (reaching ~ 100,000 electrons) on both many-core CPU and hybrid CPU-GPU computing architectures. This work involves improvements in the real-space formulation—via an improved treatment of the electrostatic interactions that substantially enhances the computational efficiency—as well high-performance computing aspects, including the GPU acceleration of all the key compute kernels in DFT-FE. We demonstrate the accuracy by comparing the ground-state energies, ionic forces and cell stresses on a wide-range of benchmark systems against those obtained from widely used DFT codes. Further, we demonstrate the numerical efficiency of our implementation, which yields ~ 20× CPU-GPU speed-up by using GPU acceleration on hybrid CPU-GPU nodes. Notably, owing to the parallel-scaling of the GPU implementation, we obtain wall-times of 80–140 seconds for full ground-state calculations, with stringent accuracy, on benchmark systems containing ~ 6, 000 – 15,000 electrons.

pseudopotential↗
DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Mixed-Precision S/DGEMM Using the TF32 and TF64 Frameworks on Low-Precision AI Tensor Cores

Using NVIDIA graphics processing units (GPUs) equipped with Tensor Cores has enabled the significant acceleration of general matrix multiplication (GEMM) for applications in machine learning (ML) and artificial intelligence (AI) and in high-performance computing (HPC) generally. The use of such power-efficient, specialized accelerators can provide a performance increase between 8 × and 20 ×, albeit with a loss in precision. However, a high level of precision is required in many large scientific and HPC applications, and computing in single or double precision is still necessary for many of these applications to maintain accuracy. Fortunately, mixed-precision methods can be employed to maintain a higher level of numerical precision while also taking advantage of the performance increases from computing with lower-precision AI cores. With this in mind, we extend the state of the art by using NVIDIA’s new TF32 framework. This new framework not only burdens some constraints of the previous frameworks, such as costly 32 16-bit castings but also provides an equivalent precision and performance by using a much simpler approach. We also propose a new framework called TF64 that attempts double-precision arithmetic with low-precision Tensor Cores. Although this framework does not exist yet, we validated the correctness of this idea and achieved an equivalent of 64-bit precision on 32-bit hardware.

Valero Lara, Pedro↗