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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 OSTI2020

Initial Exploration of the Use of Mixed Precision in Iterative Solvers (B639388 Subcontract Quarter I Report)

The first quarter of the project was primarily spent identifying potential projects at the intersection of finite precision analysis, mixed precision computation, and Krylov subspace methods. We summarize our findings in the remainder of the document. Other activities include attending biweekly xSDK meetings as well as contributing material to the technical report and journal versions of the multiprecision landscape paper. The subsequent quarter will be spent selecting a subset of the described projects to focus on, performing initial numerical experiments to evaluate the potential for the use of mixed precision, and developing initial theoretical analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms

Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speedups and lower storage cost if applied appropriately. The growing interest in employing mixed precision computations motivates the need for rounding error analysis that properly handles behavior from mixed precision arithmetic. We develop mixed precision variants of existing Householder QR algorithms and show error analyses supported by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Advances in Mixed Precision Algorithms: 2021 Edition

Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are: Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; results and strategies for mixed precision IR using a sparse LU factorization; a mixed precision eigenvalue solver; Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; preparing hypre for mixed precision execution; mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; and detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase the accuracy by using high precision in the computations without degrading the performance. We emphasize that many of the highlights presented here have also been submitted to peer-reviewed journals or established conferences, and are under peer-review or have already been published.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Advances in Mixed Precision Algorithms: 2021 Edition

Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are • Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; • Results and strategies for mixed precision IR using a sparse LU factorization; • A mixed precision eigenvalue solver; • Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; • Compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; • Preparing hypre for mixed precision execution; • Mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; • Detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase the accuracy by using high precision in the computations without degrading the performance. We emphasize that many of the highlights presented here have also been submitted to peer-reviewed journals or established conferences, and are under peer-review or have already been published.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A survey of numerical linear algebra methods utilizing mixed-precision arithmetic

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this study, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Mixed-precision numerics in scientific applications: survey and perspectives

The explosive demand for artificial intelligence (AI) workloads has led to a significant increase in silicon area dedicated to lower-precision computations on recent high-performance computing hardware designs. However, mixed-precision capabilities, which can achieve performance improvements of up to 8x compared to double-precision in extreme compute-intensive workloads, remain largely untapped in most scientific applications. A growing number of efforts have shown that mixed-precision algorithmic innovations can deliver superior performance without sacrificing accuracy. These developments should prompt computational scientists to seriously consider whether their scientific modeling and simulation applications could benefit from the acceleration offered by new hardware and mixed-precision algorithms. In this survey, we (1) review progress across diverse scientific domains—fluid dynamics, weather and climate, quantum chemistry, and computational genomics—that have begun adopting mixed-precision strategies; (2) examine state-of-the-art algorithmic techniques such as iterative refinement, splitting and emulation schemes, and adaptive precision solvers; (3) assess their implications for accuracy, performance, and resource utilization; and (4) survey the emerging software ecosystem that enables mixed-precision methods at scale. We conclude with perspectives and recommendations on cross-cutting opportunities, domain-specific challenges, and the role of co-design between application scientists, numerical analysts, and computer scientists. Collectively, this survey underscores that mixed-precision numerics can reshape computational science by aligning algorithms with the evolving landscape of hardware capabilities.

Graphics processing units↗
DOE OSTI2022

Towards Precision-Aware Fault Tolerance Approaches for Mixed-Precision Applications

Graphics Processing Units (GPUs), the dominantly adopted accelerators in HPC systems, are susceptible to transient hardware fault. New generation of GPUs feature mixed-precision architectures such as NVIDIA Tensor Cores to accelerate matrix multiplications. While being widely adapted, how would they behave under transient hardware faults remain unclear. In this study, we conduct a large-scale fault injection experiments on GEMM kernels implemented with different floating-point data types on the V100 and A100 Tensor Cores, and show distinct error resilience characteristics for the GEMMS with different formats. In the future, we plan to explore this space by building precision-aware floating-point fault tolerance techniques for applications such as DNNs that exercise low-precision computations.

Fang, Bo↗
DOE OSTI2025

Scaling the memory wall using mixed-precision - HPG-MxP on an exascale-class machine

Mixed-precision algorithms have been proposed as a way for scientific computing to benefit from some of the gains seen for AI on recent high performance computing (HPC) platforms. A few applications dominated by dense matrix operations have seen substantial speedups by utilizing low precision formats such as FP16. However, a majority of scientific simulation applications are memory bandwidth limited. Beyond preliminary studies, the practical gain from using mixed-precision algorithms on a given high-performance computing (HPC) system is largely unclear. The High Performance GMRES Mixed Precision (HPG-MxP) benchmark has been proposed to measure the useful performance of a HPC system on sparse matrix-based mixed-precision applications. In this work, we present an implementation of the HPG-MxP benchmark for an exascale system and describe our algorithm enhancements. We show for the first time a speedup of 1.6x using a combination of double- and single-precision keeping the same residual level on modern GPU-based supercomputers.

Kashi, Aditya [ORNL] (ORCID:0000000325893792)↗
DOE OSTI2022

Climbing the Summit and Pushing the Frontier of Mixed Precision Benchmarks at Extreme Scale

The rise of machine learning (ML) applications and their use of mixed precision to perform interesting science are driving forces behind AI for science on HPC. The convergence of ML and HPC with mixed precision offers the possibility of transformational changes in computational science. The HPL-AI benchmark is designed to measure the performance of mixed precision arithmetic as opposed to the HPL benchmark which measures double precision performance. Pushing the limits of systems at extreme scale is nontrivial -little public literature explores optimization of mixed precision computations at this scale. In this work, we demonstrate how to scale up the HPL-AI benchmark on the pre-exascale Summit and exascale Frontier systems at the Oak Ridge Leadership Computing Facility (OLCF) with a cross-platform design. We present the implementation, performance results, and a guideline of optimization strategies employed for delivering portable performance on both AMD and NVIDIA GPUs at extreme scale.

Lu, Hao↗
DOE OSTI2023

Differentiable Neural Architecture, Mixed Precision and Accelerator Co-Search

Quantization, effective Neural Network architecture, and efficient accelerator hardware are three important design paradigms to maximize accuracy and efficiency. Mixed Precision Quantization is a process of assigning different precision to different Neural Network layers for optimized inference. Neural Architecture Search (NAS) is a process of automatically designing the neural network for a task and can also be extended to search for the precision of each weight and activation matrix. In this paper, we develop the following three methods: (i) Fast Differentiable Hardware-aware Mixed Precision Quantization Search method to find optimal precision, (ii) Joint Differentiable hardware-aware Architecture and Mixed Precision Quantization Co-search, (iii) Joint Accelerator, Architecture, and Precision triple co-search to find best possibilities in all the three worlds. We demonstrate the effectiveness of our proposed methods targeting Bitfusion accelerator by searching mixed precision models on MobilenetV2. We achieve better accuracy-latency trade-off models than the manually designed and previously proposed search methods.

97 MATHEMATICS AND COMPUTING↗
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 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 OSTI2025

A GPU Accelerated Mixed‐Precision Finite Difference Informed Random Walker (FDiRW) Solver for Strongly Inhomogeneous Diffusion Problems

In nature, many complex multi‐physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU‐accelerated, mixed‐precision configuration for the FDiRW solver to maximize efficiency through GPU multi‐threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU‐accelerated mixed‐precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU‐accelerated mixed‐precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium‐sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Mixed precision s –step Lanczos and conjugate gradient algorithms

Compared to the classical Lanczos algorithm, the s-step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iteration. However, this comes at a price; despite being mathematically equivalent, the s-step variant may behave quite differently in finite precision, potentially exhibiting greater loss of accuracy and slower convergence relative to the classical algorithm. It has previously been shown that the errors in the s-step version follow the same structure as the errors in the classical algorithm, but are amplified by a factor depending on the square of the condition number of the O(s)-dimensional Krylov bases computed in each outer loop. As the condition number of these s-step bases grows (in some cases very quickly) with s, this limits the s values that can be chosen and thus can limit the attainable performance. In this work, we show that if a select few computations in s-step Lanczos are performed in double the working precision, the error terms then depend only linearly on the conditioning of the s-step bases. This has the potential for drastically improving the numerical behavior of the algorithm with little impact on per-iteration performance. Our numerical experiments demonstrate the improved numerical behavior possible with the mixed precision approach, and also show that this improved behavior extends to mixed precision s-step CG. Here, we present preliminary performance results on NVIDIA V100 GPUs that show that the overhead of extra precision is minimal if one uses precisions implemented in hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

OpenMxP-Opensource Mixed Precision Computing

This is an opensource library for benchmarking the system's GPU mixed precision capabilities. The software calculates solution of the system of linear equation in 64bit accuracy using mixed precision techniques and iterative refinement. Original benchmark designed is done by ICL, and it is name HPL-MxP (HPL-AI)

Lu, Hao↗
DOE OSTI2022

Multistage mixed precision iterative refinement

Abstract Low precision arithmetic, in particular half precision (16‐bit) floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings in energy. Motivated by this, there has been a renewed interest in mixed precision iterative refinement schemes for solving linear systems , and new variants of GMRES‐based iterative refinement have been developed. Each particular variant with a given combination of precisions leads to different condition number‐based constraints for convergence of the backward and forward errors, and each has different performance costs. The constraints for convergence given in the literature are, as an artifact of the analyses, often overly strict in practice, and thus could lead a user to select a more expensive variant when a less expensive one would have sufficed. In this work, we develop a multistage mixed precision iterative refinement solver which aims to combine existing mixed precision approaches to balance performance and accuracy and improve usability. For a user‐specified initial combination of precisions, the algorithm begins with the least expensive approach and convergence is monitored via inexpensive computations with quantities produced during the iteration. If slow convergence or divergence is detected using particular stopping criteria, the algorithm switches to use a more expensive, but more reliable variant. A novel aspect of our approach is that, unlike existing implementations, our algorithm first attempts to use “stronger” GMRES‐based solvers for the solution update before resorting to increasing the precision(s). In some scenarios, this can avoid the need to refactorize the matrix in higher precision. We perform extensive numerical experiments on a variety of random dense problems and problems from real applications which confirm the benefits of the multistage approach.

Oktay, Eda↗
DOE OSTI2021

Mixed Precision xsdk Project. Final Report

Two main tasks have been performed in the past year as part of the Mixed Precision xsdk Project: analysis and development of mixed precision algorithms, and community engagement. Each is briefly discussed and work summarized.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Understanding Mixed Precision GEMM with MPGemmFI: Insights into Fault Resilience

Emerging deep learning workloads urgently need fast general matrix multiplication (GEMM). Thus, one of the critical features of machine-learning-specific accelerators such as NVIDIA Tensor Cores, AMD Matrix Cores, and Google TPUs is the support of mixed-precision enabled GEMM. For DNN models, lower-precision FP data formats and computation offer acceptable correctness but significant performance, area, and memory footprint improvement. While promising, the mixed-precision computation on error resilience remains unexplored. To this end, we develop a fault injection framework that systematically injects fault into the mixed-precision computation results. We investigate how the faults affect the accuracy of machine learning applications. Based on the characteristics of error resilience, we offer lightweight error detection and correction solutions that significantly improve the overall model accuracy by 75% if the models experience hardware faults. The solutions can be efficiently integrated into the accelerator's pipelines.

Fang, Bo↗