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Accelerating numerical solution of stochastic differential equations with CUDA

机译：用CUDA加速随机微分方程的数值解

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摘要

Numerical integration of stochastic differential equations is commonly used in many branches of science. In this paper we present how to accelerate this kind of numerical calculations with popular NVIDIA Graphics Processing Units using the CUDA programming environment. We address general aspects of numerical programming on stream processors and illustrate them by two examples: the noisy phase dynamics in a Josephson junction and the noisy Kuramoto model. In presented cases the measured speedup can be as high as 675× compared to a typical CPU, which corresponds to several billion integration steps per second. This means that calculations which took weeks can now be completed in less than one hour. This brings stochastic simulation to a completely new level, opening for research a whole new range of problems which can now be solved interactively.
机译：随机微分方程的数值积分通常用于许多科学领域。在本文中，我们介绍了如何使用CUDA编程环境使用流行的NVIDIA图形处理单元来加速这种数值计算。我们讨论了流处理器上数字编程的一般方面，并通过两个示例进行了说明：约瑟夫森结中的嘈杂相位动力学和嘈杂的仓本模型。在目前的情况下，与典型的CPU相比，测得的加速比可以高达675倍，相当于每秒数十亿个集成步骤。这意味着耗时数周的计算现在可以在不到一小时的时间内完成。这将随机模拟提高到一个全新的水平，为研究提供了一个全新的范围，现在可以交互解决。

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