Sodecl

Abstract

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 SODECL (https://github.com/avramidis/sodecl), a software library that utilizes 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 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 ≈6.7, compared to when using a single CPU core. Executing the task on a high-end GPU yielded accelerations of up to ≈4.5, compared to a single CPU core. CCS Concepts: • Theory of computation → Massively parallel algorithms; • Hardware → Testing with distributed and parallel systems; • Software and its engineering → Software libraries and repositories;

An Analysis of Approximation Algorithms for Iterated Stochastic Integrals and a Julia and MATLAB Simulation Toolbox

“…There exist several software packages to simulate SDEs available in various programming languages. A short search brought up the following 20 toolboxes: for the C++ programming language [4,25], for the Julia programming language [2,48,49,50], for Mathematica [54], for Matlab [17,22,44,52], for the Python programming language [1,3,15,16,36] and for the R programming language [6,18,23,24]. However, only four of these toolboxes seem to contain an implementation of an approximation for the iterated stochastic integrals using Wiktorsson's algorithm and none of them provide an implementation of the recently proposed Mrongowius-Rößler algorithm.…”