SIAM Journal on Scientific Computing, Volume 43, Issue 5, Page A3135-A3154, January 2021.
In this paper, we introduce a numerical method for nonlinear parabolic partial differential equations (PDEs) that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small, the approach can handle extremely high dimensional PDEs. We test the method on different examples from physics, stochastic control, and mathematical finance. In all cases, it yields very good results in up to 10,000 dimensions with short run times.

中文翻译：

---

抛物线偏微分方程的深度分裂方法

SIAM Journal on Scientific Computing，第 43 卷，第 5 期，第 A3135-A3154 页，2021
年1 月。在本文中，我们介绍了一种结合算子分裂和深度学习的非线性抛物偏微分方程 (PDE) 数值方法。它将 PDE 逼近问题划分为一系列单独的学习问题。由于每个子问题的计算图相对较小，因此该方法可以处理极高维的 PDE。我们在来自物理学、随机控制和数学金融的不同示例上测试该方法。在所有情况下，它都能在较短的运行时间内在多达 10,000 个维度上产生非常好的结果。