On the use of programmable hardware and reduced numerical precision in earth‐system modeling

Abstract

Programmable hardware, in particular Field Programmable Gate Arrays (FPGAs), promises a significant increase in computational performance for simulations in geophysical fluid dynamics compared with CPUs of similar power consumption. FPGAs allow adjusting the representation of floating-point numbers to specific application needs. We analyze the performance-precision trade-off on FPGA hardware for the two-scale Lorenz '95 model. We scale the size of this toy model to that of a high-performance computing application in order to make meaningful performance tests. We identify the minimal level of precision at which changes in model results are not significant compared with a maximal precision version of the model and find that this level is very similar for cases where the model is integrated for very short or long intervals. It is therefore a useful approach to investigate model errors due to rounding errors for very short simulations (e.g., 50 time steps) to obtain a range for the level of precision that can be used in expensive long-term simulations. We also show that an approach to reduce precision with increasing forecast time, when model errors are already accumulated, is very promising. We show that a speed-up of 1.9 times is possible in comparison to FPGA simulations in single precision if precision is reduced with no strong change in model error. The single-precision FPGA setup shows a speed-up of 2.8 times in comparison to our model implementation on two 6-core CPUs for large model setups.

Testing the Numerical Precisions Required to Execute Real World Programs

“…The implication of this study, and of the studies by Düben et al [2015] [7] and Dawson and Düben [2016] [8] are that lower precision number formats with shorter word lengths would be of considerable value. These would provide improvements in computational speed through faster arithmetic, and through improved packing of data in cache and in inter-processor communication.…”

“…There are also significant savings in cache coherence and inter-processor communication where lower precisions can be used, because the numbers occupy less memory. Düben and Palmer [2014] [6], Düben et al [2015] [7] and Dawson and Düben, [2016] [8] tested the use of reduced precision numbers in small atmospheric codes, and found that the performance is resilient to reductions in precision significantly below the 23 mantissa bits in 32-bit IEEE 754 numbers. The urgent need and economic justification for greatly increased computing power in weather and climate prediction is well described by Shukla et al [2010] [9].…”

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

“…Recent work [3,4,5,6] and [7] has explored the potential benefits of moving away from the use of 64-bit arithmetic throughout an atmospheric model. These papers examine a variety of approaches to reducing precision, from low precision emulators, Field Programmable Gate Arrays (FPGAs), toy models, right through to running a full atmospheric model in 32-bit precision (i.e.…”

An Objective and Efficient Method for Assessing the Impact of Reduced‐Precision Calculations On Solution Correctness

“…This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. studies by, for example, Düben et al (2014), Düben et al (2015), and Nakano et al (2018), used the Lorenz' 96 model, dynamical cores of global atmospheric models, and general circulation models of intermediate complexity to demonstrate that satisfactory simulation quality can be achieved with lower-precision arithmetic. The European Centre for Medium-range Weather Forecasts has implemented a 32-bit (single-precision) version of their Integrated Forecast System that provides the same quality in medium-range ensemble forecasts but uses 40% less computing time compared to the double-precision version (Ván a et al, 2017).…”