Cost-effective massive computational speedups in simulations of high dimensional dynamical systems

This is the authors' abstract. We don't add key points for this paper.

High dimensional dynamical systems involve a large number of coupled, generally nonlinear, differential equations that are computationally intensive to simulate, thus requiring expensive computational resources. This paper presents a novel strategy for numerically integrating such systems by utilizing cheaper gaming GPUs and mixed-precision computations. This is facilitated by exploiting the higher single-precision floating-point throughput of gaming GPUs and their relatively cheaper costs which enable packing multiple gaming GPUs into a single compute node. Appropriately parallelizing the algorithm and using mixed-precision computation enables massive computational speedup without severely compromising on accuracy. The potential of these developments is illustrated through a representative high dimensional dynamical system which shows a massive speedup over serial execution, even exceeding 1000-fold for larger-scale systems. These developments have the potential to make a substantial impact on the simulation and exploration of dynamical systems at massive scales without the need for expensive hardware resources.