Accelerating numerical solution of Stochastic Differential Equations with CUDA

TL;DR

This paper demonstrates how leveraging CUDA on NVIDIA GPUs can massively accelerate the numerical integration of stochastic differential equations, enabling faster and more interactive simulations in scientific research.

Contribution

It introduces methods for GPU acceleration of stochastic differential equations and provides practical examples with significant speedup results.

Findings

Speedup up to 675x compared to CPU

Enables billion-step simulations in under an hour

Facilitates interactive stochastic research

Abstract

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 675x 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.