论文标题
BSDE的深runge-kutta计划
Deep Runge-Kutta schemes for BSDEs
论文作者
论文摘要
我们提出了一种新的概率方案，该方案将深度学习技术与属于runge-kutta方法类别的后退随机微分方程相结合，以求解高维半线性抛物线部分偏微分方程。我们的方法特别扩展了[Hure Pham Warin 2020]中的隐式Euler方案中引入的方法，该方案降至离散时间误差方面更有效的方案。我们在经典规律性假设下为我们实施的方案建立了一些融合结果。我们还说明了我们方法对一，二和三的不同方案的效率。我们的数值结果表明，就精确，计算成本和数值实施而言，曲柄 - 尼古尔森方案是一个很好的妥协。
We propose a new probabilistic scheme which combines deep learning techniques with high order schemes for backward stochastic differential equations belonging to the class of Runge-Kutta methods to solve high-dimensional semi-linear parabolic partial differential equations. Our approach notably extends the one introduced in [Hure Pham Warin 2020] for the implicit Euler scheme to schemes which are more efficient in terms of discrete-time error. We establish some convergence results for our implemented schemes under classical regularity assumptions. We also illustrate the efficiency of our method for different schemes of order one, two and three. Our numerical results indicate that the Crank-Nicolson schemes is a good compromise in terms of precision, computational cost and numerical implementation.
