Validating optimisations for chaotic simulations

Abstract

Abstract-It is non-trivial to optimise computations of chaotic systems since slightly perturbed simulations diverge exponentially over time due to the well-known butterfly effect if bit-reproducible results are not achieved. Therefore, two model setups that show the same quality in the representation of a chaotic system will show uncorrelated behaviour if integrated long enough, hence it is challenging to check whether a given optimisation degrades model quality. Most models in computational fluid dynamics show chaotic behaviour. In this paper we focus on models of atmosphere and ocean that are vital for predictions of future weather and climate. Since forecast quality is usually limited by the available computational power, optimisation is highly desirable. We describe a new method for accepting or rejecting an optimised implementation of a reconfigurable design to simulate dynamics of a chaotic system. We apply this method to optimise numerical precision to a minimal level of stencil computations that can be used in an idealised ocean model, and show the performance improvements gained on an FPGA. The proposed method enables precision reduction for the FPGA so that it computes up to 9 times faster with 6 times lower energy consumption than an implementation on the same device with double precision arithmetic, while ensuring the optimised design to have acceptable numerical behaviour.

Discriminating accurate results in nonlinear models

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