Stochastic differential equations (SDEs) are widely used to model systems affected by random processes. In general, the analysis of an SDE model requires numerical solutions to be generated many times over multiple parameter combinations. However, this process often requires considerable computational resources to be practicable. Due to the embarrassingly parallel nature of the task, devices such as multi-core processors and graphics processing units (GPUs) can be employed for acceleration. Here, we present {\bf SODECL} (\url{https://github.com/avramidis/sodecl}), a software library that utilises such devices to calculate multiple orbits of an SDE model. To evaluate the acceleration provided by SODECL, we compared the time required to calculate multiple orbits of an exemplar stochastic model when one CPU core is used, to the time required when using all CPU cores or a GPU. In addition, to assess scalability, we investigated how the model size affected execution time on different parallel compute devices. Our results show that when using all 32 CPU cores of a high-end high-performance computing node, the task is accelerated by a factor of up to $\simeq$6.7, compared to when using a single CPU core. Executing the task on a high-end GPU yielded accelerations of up to $\simeq$4.5, compared to a single CPU core.

中文翻译：

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SODECL：用于并行计算随机微分方程系统的多个轨道的开源库

随机微分方程 (SDE) 被广泛用于模拟受随机过程影响的系统。通常，SDE 模型的分析需要针对多个参数组合多次生成数值解。然而，该过程通常需要相当多的计算资源才能实施。由于任务的并行性令人尴尬，因此可以使用多核处理器和图形处理单元 (GPU) 等设备进行加速。在这里，我们展示了 {\bf SODECL} (\url{https://github.com/avramidis/sodecl})，这是一个利用此类设备计算 SDE 模型的多个轨道的软件库。为了评估 SODECL 提供的加速度，我们比较了使用一个 CPU 内核时计算示例随机模型的多个轨道所需的时间，到使用所有 CPU 内核或 GPU 所需的时间。此外，为了评估可扩展性，我们调查了模型大小如何影响不同并行计算设备上的执行时间。我们的结果表明，当使用高端高性能计算节点的所有 32 个 CPU 内核时，与使用单个 CPU 内核时相比，任务加速高达 $\simeq$6.7。与单个 CPU 内核相比，在高端 GPU 上执行任务可产生高达 $\simeq$4.5 的加速。