论文标题
随机瘫痪算法的错误结合分析
Error bound analysis of the stochastic parareal algorithm
论文作者
论文摘要
随机瘫痪（Sparareal）是流行的平行算法的概率变体，称为Parareal。与瘫痪类似，它使用预测器 - 校正器（PC）方案将细粒和粗粒溶液结合到普通微分方程（ODE）。关键区别在于，精心选择的随机扰动被添加到PC中，以尝试加速随机解决方案到ODE的位置。在本文中，我们使用不同类型的扰动将频施加到ODE的非线性系统上的频源性的超线性和线性均方误差界限。我们在数值上说明这些界限在ODE和标量非线性颂歌的线性系统上，显示了理论和数字之间的良好匹配。
Stochastic parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as parareal. Similarly to parareal, it combines fine- and coarse-grained solutions to an ordinary differential equation (ODE) using a predictor-corrector (PC) scheme. The key difference is that carefully chosen random perturbations are added to the PC to try to accelerate the location of a stochastic solution to the ODE. In this paper, we derive superlinear and linear mean-square error bounds for SParareal applied to nonlinear systems of ODEs using different types of perturbations. We illustrate these bounds numerically on a linear system of ODEs and a scalar nonlinear ODE, showing a good match between theory and numerics.
