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

Paper: arXiv 2302.05170

Authors: Shuaiqiang Liu, Graziana Colonna, Lech A. Grzelak, Cornelis W. Oosterlee

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.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a solid mathematical extension of the Seven-League Scheme by adapting it to GPU-based parallel execution for Monte Carlo simulations of SDEs. While the core deep learning architecture is based on existing literature, the focus on computational efficiency and GPU parallelization offers meaningful empirical gains in execution speed for large time steps.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Accelerate Seven-League Scheme for SDEs via GPU Parallelism"] --> B["Data & Inputs:<br>SDE Parameters & Deep Neural Network Configurations"]
    B --> C["Methodology:<br>Generalize Scheme for GPU Architecture"]
    C --> D["Computational Process:<br>Batch Deep Learning Inference & Monte Carlo Simulations on GPUs"]
    D --> E["Key Outcomes:<br>High-Accuracy SDE Solutions with Large Time Steps & Significant Speedup"]