Exploiting the chaotic behaviour of atmospheric models with reconfigurable architectures

Russell, Francis P.; Dueben, Peter; Niu, Xinyu; Luk, Wayne; Palmer, Tim

doi:10.1016/j.cpc.2017.08.011

Cited by 15 publications

(12 citation statements)

References 21 publications

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“…This indicates problems for reduced precision modelling: Rescaling of the equations is desired to place many arithmetic calculations near the largest representable number, however, any result beyond will lead to disastrous results, as integer overflow usually returns a negative value following a wrap around behaviour. Flexibility regarding the dynamic range can be achieved with integer arithmetic if fixed point numbers are used [26]. However, we did not achieve convincing results with integer arithmetic for the applications in this paper (see section 3.2).…”

Section: Decimal Precisionmentioning

confidence: 63%

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Posits as an alternative to floats for weather and climate models

Klöwer

Dueben

Palmer

2019

Proceedings of the Conference for Next Generation Arithmetic 2019

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Posit numbers, a recently proposed alternative to floating-point numbers, claim to have smaller arithmetic rounding errors in many applications. By studying weather and climate models of low and medium complexity (the Lorenz system and a shallow water model) we present benefits of posits compared to floats at 16 bit. As a standardised posit processor does not exist yet, we emulate posit arithmetic on a conventional CPU. Using a shallow water model, forecasts based on 16-bit posits with 1 or 2 exponent bits are clearly more accurate than half precision floats. We therefore propose 16 bit with 2 exponent bits as a standard posit format, as its wide dynamic range of 32 orders of magnitude provides a great potential for many weather and climate models. Although the focus is on geophysical fluid simulations, the results are also meaningful and promising for reduced precision posit arithmetic in the wider field of computational fluid dynamics.

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Section: Decimal Precisionmentioning

confidence: 63%

“…This comes with the disadvantage that simulations are orders of magnitude slower. However, software emulation allows a scientific evaluation of the use of reduced numerical precision for weather and climate simulations with no need to port the models to special hardware (such as FPGAs, [26]).…”

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confidence: 99%

Posits as an alternative to floats for weather and climate models

Klöwer

Dueben

Palmer

2019

Proceedings of the Conference for Next Generation Arithmetic 2019

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“…Software emulators for other number formats than Float32 and Float64 are often used to investigate rounding errors caused by lower‐precision formats (Dawson & Düben, 2017). Although emulators are considerably slower than hardware‐accelerated formats, they allow a scientific evaluation of the introduced errors without requiring specialized hardware, such as field‐programmable gate arrays (FPGAs, Russell et al., 2017). Unfortunately, the computational performance cannot be assessed with software emulators.…”

Section: Introductionmentioning

confidence: 99%

Number Formats, Error Mitigation, and Scope for 16‐Bit Arithmetics in Weather and Climate Modeling Analyzed With a Shallow Water Model

Klöwer

Dueben

Palmer

2020

J Adv Model Earth Syst

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The need for high-precision calculations with 64-bit or 32-bit floating-point arithmetic for weather and climate models is questioned. Lower-precision numbers can accelerate simulations and are increasingly supported by modern computing hardware. This paper investigates the potential of 16-bit arithmetic when applied within a shallow water model that serves as a medium complexity weather or climate application. There are several 16-bit number formats that can potentially be used (IEEE half precision, BFloat16, posits, integer, and fixed-point). It is evident that a simple change to 16-bit arithmetic will not be possible for complex weather and climate applications as it will degrade model results by intolerable rounding errors that cause a stalling of model dynamics or model instabilities. However, if the posit number format is used as an alternative to the standard floating-point numbers, the model degradation can be significantly reduced. Furthermore, mitigation methods, such as rescaling, reordering, and mixed precision, are available to make model simulations resilient against a precision reduction. If mitigation methods are applied, 16-bit floating-point arithmetic can be used successfully within the shallow water model. The results show the potential of 16-bit formats for at least parts of complex weather and climate models where rounding errors would be entirely masked by initial condition, model, or discretization error. Plain Language Summary 64-bit floating-point numbers are the standard number format for scientific computing in fluid dynamics, which allows for very precise calculations with negligible rounding errors. The need for calculations at this precision level has been questioned for weather and climate models, as errors are caused primarily by insufficient observations or deficiencies of the models themselves. Reducing numerical precision can accelerate simulations and low-precision number formats are increasingly supported by modern computers. This paper investigates the potential of low numerical precision with numbers that only use 16 bit of information, when applied within simulations of weather and climate. The different number formats are applied in a two-dimensional oceanic or atmospheric circulation model. There are several 16-bit number formats that can potentially be used, all of which have considerably larger rounding errors than the standard 64-bit numbers. A simple change to 16 bits for all calculations will not be possible as it will degrade simulation results. However, if mitigation methods are applied, 16-bit calculations can be used successfully within the applications of this paper. The results show the potential of 16-bit number formats for at least parts of complex weather and climate models.

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“…This property is described as butterfly effect in the available literature which is observed by Lorenz [1] in 1963 while studying a simplified model of convection for weather predictions. Chaos theory has a wide range of applications in numerous areas of engineering and applied sciences, for example, jerk systems [2], robotics [3], finance models [4], weather models [5], ecological models [6], chemical reactions [7], circuits [8], oscillations [9], encryption [10], neural networks [11], biomedical engineering [12] etc. Consequently, chaos synchronization and control of nonlinear chaotic systems attracts researchers as well as academicians from various scientific fields in the recent years.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Projective Synchronization of 4-D Hyperchaotic Systems via Adaptive Control

Khan

Chaudhary

2020

J. Sci. Res.

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This paper designs a procedure for investigating the hybrid projective synchronization (HPS) scheme between two identical 4-D hyperchaotic systems. Based on Lyapunov stability theory (LST), an adaptive control technique (ACT) has been designed to achieve the desired HPS scheme. The suggested technique determines globally the asymptotic stability and identification of parameters simultaneously using HPS scheme. It is noted that complete , hybrid and anti-synchronization turns into particular cases of HPS scheme. Numerical simulations are presented to validate the effectivity and feasibleness of the considered technique by using MATLAB. Remarkably, the theoretical and computational outcomes are in complete agreement. Also, the considered HPS scheme is very efficient as it has numerous applications in encryption and secure communication.

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Exploiting the chaotic behaviour of atmospheric models with reconfigurable architectures

Cited by 15 publications

References 21 publications

Posits as an alternative to floats for weather and climate models

Posits as an alternative to floats for weather and climate models

Number Formats, Error Mitigation, and Scope for 16‐Bit Arithmetics in Weather and Climate Modeling Analyzed With a Shallow Water Model

Hybrid Projective Synchronization of 4-D Hyperchaotic Systems via Adaptive Control

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