Mixed-precision arithmetic in the ENDGame dynamical core of the Unified Model, a numerical weather prediction and climate model code

Maynard, Christopher M.; Walters, David

doi:10.1016/j.cpc.2019.07.002

Cited by 15 publications

(16 citation statements)

References 19 publications

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“…In [20], the authors show how single-and half-precision can replace full double-precision calculations for weather and climate applications which can maintain the desirable accuracy at the end. In [21], mixed-precision Krylov sub-space solver for climate/weather applications has been proposed. The study shows numerical instabilities that impact the accuracy of prediction.…”

Section: Related Workmentioning

confidence: 99%

“…Nested Block Cyclic Data Distributions. Porting the ExaGeoStat_PaRSEC as well as mixed-precision Cholesky proposed here is implemented with complete GPU support, i.e., distributed multi-GPUs, making it more prominent than most of those about mixed-precision in the related works [4], [21]- [23], [25], [52]. PaRSEC automatically handles asynchronous data transfers between hosts and devices to overlap data movement with computations, and also provides data locality scheduling policies to reduce communications and improve load balancing.…”

Section: Parsec Runtime Optimizationsmentioning

confidence: 99%

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Accelerating Geostatistical Modeling and Prediction With Mixed-Precision Computations: A High-Productivity Approach With PaRSEC

Abdulah

Cao

Pei

et al. 2022

IEEE Trans. Parallel Distrib. Syst.

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Geostatistical modeling, one of the prime motivating applications for exascale computing, is a technique for predicting desired quantities from geographically distributed data, based on statistical models and optimization of parameters. Spatial data is assumed to possess properties of stationarity or non-stationarity via a kernel fitted to a covariance matrix. A primary workhorse of stationary spatial statistics is Gaussian maximum log-likelihood estimation (MLE), whose central data structure is a dense, symmetric positive definite covariance matrix of dimension of the number of correlated observations. Two essential operations in MLE are the application of the inverse and evaluation of the determinant of the covariance matrix. These can be rendered through the Cholesky decomposition and triangular solution. In this contribution, we reduce the precision of weakly correlated locations to single-or half-precision based on distance. We thus exploit mathematical structure to migrate MLE to a three-precision approximation that takes advantage of contemporary architectures offering BLAS3-like operations in a single instruction that are extremely fast for reduced precision. We illustrate application-expected accuracy worthy of doubleprecision from a majority half-precision computation, in a context where uniform single precision is by itself insufficient. In tackling the complexity and imbalance caused by the mixing of three precisions, we deploy the PaRSEC runtime system. PaRSEC delivers on-demand casting of precisions while orchestrating tasks and data movement in a multi-GPU distributed-memory environment within a tile-based Cholesky factorization. Application-expected accuracy is maintained while achieving up to 1.59X by mixing FP64/FP32 operations on 1536 nodes of HAWK or 4096 nodes of Shaheen II, and up to 2.64X by mixing FP64/FP32/FP16 operations on 128 nodes of Summit, relative to FP64-only operations, This translates into up to 4.5, 4.7, and 9.1 (mixed) PFlop/s sustained performance, respectively, demonstrating a synergistic combination of exascale architecture, dynamic runtime software, and algorithmic adaptation applied to challenging environmental problems.

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Section: Related Workmentioning

confidence: 99%

Section: Parsec Runtime Optimizationsmentioning

confidence: 99%

Accelerating Geostatistical Modeling and Prediction With Mixed-Precision Computations: A High-Productivity Approach With PaRSEC

Abdulah

Cao

Pei

et al. 2022

IEEE Trans. Parallel Distrib. Syst.

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“…Based on our overall experience with W&C models, in this paper = 10 −5 is assumed for all experiments. We also enforce at least one full GCR(3) cycle regardless of (13). Further discussion and justification for this choice of is found in §4.1.…”

Section: The Elliptic Solvermentioning

confidence: 99%

“…Early work on thorough analysis to identify the minimal level of numerical precision that can be used in different parts of dycores has focused on spectral model formulations [9,10]. Similar work on grid-point model formulations has only just begun with the use of single precision arithmetic [11,12,13] with 32 bits per variable.…”

Section: Introductionmentioning

confidence: 99%

“…To efficiently solve an elliptic problem posed in a thin spherical shell (such as the global atmosphere) ultimately requires matrix inversion-if not in the main solver than at least in its preconditioner. While there is the common opinion that high precision is required for this purpose, there are theoretical studies [2,3,28,29,30] suggesting that mixed-precision approaches could be exploited, and there are already some applications of mixed-precision elliptic solvers in CFD [31,32,4] and also in W&C [13]. Although these approaches may differ in choice of algorithms and applications, a common theme emerges that the preconditioning step may be a good choice for reducing precision, where some work goes as low as half precision arithmetic (16 bits per variable) representing each real number with only 16 bits (as a floating point number) and decimal precision reduced to three digits.…”

Section: Introductionmentioning

confidence: 99%

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Machine-Learned Preconditioners for Linear Solvers in Geophysical Fluid Flows

Ackmann¹,

Dueben²,

Palmer³

et al. 2021

Preprint

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Semi-implicit grid-point models for the atmosphere and the ocean require linear solvers that are working efficiently on modern supercomputers. The huge advantage of the semi-implicit time-stepping approach is that it enables large model time-steps. This however comes at the cost of having to solve a computationally demanding linear problem each model time-step to obtain an update to the model&#8217;s pressure/fluid-thickness field. In this study, we investigate whether machine learning approaches can be used to increase the efficiency of the linear solver.Our machine learning approach aims at replacing a key component of the linear solver&#8212;the preconditioner. In the preconditioner an approximate matrix inversion is performed whose quality largely defines the linear solver&#8217;s performance. Embedding the machine-learning method within the framework of a linear solver circumvents potential robustness issues that machine learning approaches are often criticized for, as the linear solver ensures that a sufficient, pre-set level of accuracy is reached. The approach does not require prior availability of a conventional preconditioner and is highly flexible regarding complexity and machine learning design choices.Several machine learning methods of different complexity from simple linear regression to deep feed-forward neural networks are used to learn the optimal preconditioner for a shallow-water model with semi-implicit time-stepping. The shallow-water model is specifically designed to be conceptually similar to more complex atmosphere models. The machine-learning preconditioner is competitive with a conventional preconditioner and provides good results even if it is used outside of the dynamical range of the training dataset.

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