Fluid Simulations Accelerated With 16 Bits: Approaching 4x Speedup on A64FX by Squeezing ShallowWaters.jl Into Float16.

Most Earth-system simulations run on conventional central processing units in 64-bit double precision floating-point numbers Float64, although the need for high-precision calculations in the presence of large uncertainties has been questioned. Fugaku, currently the world's fastest supercomputer, is based on A64FX microprocessors, which also support the 16-bit low-precision format Float16. We investigate the Float16 performance on A64FX with ShallowWaters.jl, the first fluid circulation model that runs entirely with 16-bit arithmetic. The model implements techniques that address precision and dynamic range issues in 16 bits. The precision-critical time integration is augmented to include compensated summation to minimize rounding errors. Such a compensated time integration is as precise but faster than mixed precision with 16 and 32-bit floats. As subnormals are inefficiently supported on A64FX the very limited range available in Float16 is 6 × 10-5 to 65,504. We develop the analysis-number format Sherlogs.jl to log the arithmetic results during the simulation. The equations in ShallowWaters.jl are then systematically rescaled to fit into Float16, using 97% of the available representable numbers. Consequently, we benchmark speedups of up to 3.8x on A64FX with Float16. Adding a compensated time integration, speedups reach up to 3.6x. Although ShallowWaters.jl is simplified compared to large Earth-system models, it shares essential algorithms and therefore shows that 16-bit calculations are indeed a competitive way to accelerate Earth-system simulations on available hardware.

Compressing atmospheric data into its real information content.

Hundreds of petabytes are produced annually at weather and climate forecast centers worldwide. Compression is essential to reduce storage and to facilitate data sharing. Current techniques do not distinguish the real from the false information in data, leaving the level of meaningful precision unassessed. Here we define the bitwise real information content from information theory for the Copernicus Atmospheric Monitoring Service (CAMS). Most variables contain fewer than 7 bits of real information per value and are highly compressible due to spatio-temporal correlation. Rounding bits without real information to zero facilitates lossless compression algorithms and encodes the uncertainty within the data itself. All CAMS data are 17× compressed relative to 64-bit floats, while preserving 99% of real information. Combined with four-dimensional compression, factors beyond 60× are achieved. A data compression Turing test is proposed to optimize compressibility while minimizing information loss for the end use of weather and climate forecast data.

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

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.

On the use of inexact, pruned hardware in atmospheric modelling.

Inexact hardware design, which advocates trading the accuracy of computations in exchange for significant savings in area, power and/or performance of computing hardware, has received increasing prominence in several error-tolerant application domains, particularly those involving perceptual or statistical end-users. In this paper, we evaluate inexact hardware for its applicability in weather and climate modelling. We expand previous studies on inexact techniques, in particular probabilistic pruning, to floating point arithmetic units and derive several simulated set-ups of pruned hardware with reasonable levels of error for applications in atmospheric modelling. The set-up is tested on the Lorenz '96 model, a toy model for atmospheric dynamics, using software emulation for the proposed hardware. The results show that large parts of the computation tolerate the use of pruned hardware blocks without major changes in the quality of short- and long-time diagnostics, such as forecast errors and probability density functions. This could open the door to significant savings in computational cost and to higher resolution simulations with weather and climate models.