Acceleration of automatic differentiation of solutions to parabolic partial differential equations: a higher order discretization
Acceleration of automatic differentiation of solutions to parabolic partial differential equations: a higher order discretization
复制标题
抛物型偏微分方程解的自动微分加速：高阶离散化
DOI：
10.1007/s11075-020-00902-z
复制
发表时间：
2020
影响因子：
2.1
通讯作者：
Toshihiro Yamada
中科院分区：
文献类型：
--
作者：
Kimiki Tokutome;Toshihiro Yamada
提出了一种新的求解抛物型偏微分方程解的自动微分算法。特别地，我们提供了一个高阶离散化方案，它是标准自动微分的自然扩展。引入布朗多项式方法避免了lsamvy区域模拟。与随机微分方程相关的向量场的李括号在该格式中起着重要作用。考虑了测试函数不光滑但有门道导数的情况。数值算例验证了该方法的有效性
The paper proposes a new automatic/algorithmic differentiation for the solutions to partial differential equations of parabolic type. In particular, we provide a higher order discretization scheme which is a natural extension of the standard automatic differentiation. A Brownian polynomial approach is introduced to avoid the Lévy area simulation. The Lie brackets of vector fields associated with stochastic differential equation play an important role in the proposed scheme. The case that the test function is non-smooth but has Gateaux derivative is considered. Numerical examples are shown to confirm the effectiveness