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Uncertainty Quantification of Reduced-Precision Time Series in Turbulent Channel Flow

Workshop: 1st Workshop on Enabling Predictive Science with Optimization and Uncertainty Quantification in HPC

Authors: Martin Karp (KTH Royal Institute of Technology); Felix Liu (KTH Royal Institute of Technology, Raysearch Laboratories); Ronith Stanly (KTH Royal Institute of Technology); Saleh Rezaeiravesh (University of Manchester); Niclas Jansson (KTH Royal Institute of Technology); Philipp Schlatter (Friedrich-Alexander Universität (FAU), KTH Royal Institute of Technology); and Stefano Markidis (KTH Royal Institute of Technology)

Abstract: With increased computational power through the use of low-precision arithmetic, a relevant question is how lower precision affects simulation results, especially for chaotic systems where analytical round-off estimates are non-trivial to obtain. In this work, we consider how the uncertainty of the time series of a direct numerical simulation of turbulent channel flow at 𝑅𝑒𝜏 = 180 is affected when restricted to a reduced-precision representation. We utilize a non-overlapping batch means estimator and find that the mean statistics can, in this case, be obtained with significantly fewer mantissa bits than conventional IEEE-754 double precision, but that the mean flow is more sensitive in the middle of the channel than the boundary layer. This indicates that using lower precision in the boundary layer, where the majority of the computational work is located, may benefit significantly from low-precision floating point units found in upcoming computer hardware.

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