GPU acceleration of the Seven-League Scheme for large time step simulations of stochastic differential equations

TL;DR

This paper enhances the Seven-League scheme for stochastic differential equations by leveraging GPU parallel computing, significantly improving simulation speed while maintaining accuracy with large time steps.

Contribution

It generalizes the Seven-League scheme for GPU acceleration, enabling faster large time step simulations of stochastic differential equations.

Findings

GPU implementation speeds up simulations

Large time steps maintain accuracy

Method outperforms traditional approaches

Abstract

Monte Carlo simulation is widely used to numerically solve stochastic differential equations. Although the method is flexible and easy to implement, it may be slow to converge. Moreover, an inaccurate solution will result when using large time steps. The Seven League scheme, a deep learning-based numerical method, has been proposed to address these issues. This paper generalizes the scheme regarding parallel computing, particularly on Graphics Processing Units (GPUs), improving the computational speed.