Automatic Differentiation: Applications, Theory, and Implementations
Automatic Differentiation: Applications, Theory, and Implementations
复制标题
自动微分：应用、理论和实现
DOI：
10.1007/3-540-28438-9_4
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Christianson B
中科院分区：
文献类型：
--
作者：
Christianson B
受计量学问题的启发，我们把一个数值计算程序y=f(X)看作是一个测量过程的模型。我们使用概率密度函数来表示输入x中的不确定性，并检验了使用自动微分将这些不确定性传播到输出的一些后果。我们展示了如何使用泰勒级数传播和区间划分的组合来基于输出的均值和协方差的无偏估计来获得覆盖(置信度)区间和椭球，即使f是严重非线性的，即使所需的概率水平使得使用蒙特卡罗技术在计算上存在问题。
AbstractMotivated by problems in metrology, we consider a numerical evaluation program y = f(x) as a model for a measurement process. We use a probability density function to represent the uncertainties in the inputs x and examine some of the consequences of using Automatic Differentiation to propagate these uncertainties to the outputs y.We show how to use a combination of Taylor series propagation and interval partitioning to obtain coverage (confidence) intervals and ellipsoids based on unbiased estimators for means and covariances of the outputs, even where f is sharply non-linear, and even when the level of probability required makes the use of Monte Carlo techniques computationally problematic.