GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA

TL;DR

This paper demonstrates how CUDA-accelerated GPU computing can significantly speed up Monte Carlo simulations of Brownian motors, enabling more efficient stochastic differential equation modeling with speedups up to 3000 times over CPUs.

Contribution

It provides an extended guide for accelerating Monte Carlo integration of stochastic differential equations using CUDA on GPUs, with practical models and detailed numerical scheme discussions.

Findings

Speedup of about 3000 times compared to CPU implementations

Demonstration of GPU acceleration on models of Brownian motors with different noise types

Expanded computational capabilities for stochastic simulations

Abstract

This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases.