Algorithmic differentiation (AD), also known as automatic differentiation, is a technology for accurate and efficient evaluation of derivatives of a function given as a computer model. The evaluations of such models are essential building blocks in numerous scientific computing and data analysis applications, including optimization, parameter identification, sensitivity analysis, uncertainty quantification, nonlinear equation solving, and integration of differential equations. We provide an introduction to AD and present its basic ideas and techniques, some of its most important results, the implementation paradigms it relies on, the connection it has to other domains including machine learning and parallel computing, and a few of the major open problems in the area. Topics we discuss include: forward mode and reverse mode of AD, higher‐order derivatives, operator overloading and source transformation, sparsity exploitation, checkpointing, cross‐country mode, and differentiating iterative processes.

中文翻译：

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算法差异介绍

算法微分（AD），也称为自动微分，是一种用于准确，高效地评估作为计算机模型给出的函数的导数的技术。这种模型的评估是许多科学计算和数据分析应用程序中必不可少的组成部分，包括优化，参数识别，灵敏度分析，不确定性量化，非线性方程式求解和微分方程式集成。我们将介绍AD，并介绍其基本思想和技术，一些最重要的结果，其依赖的实现范式，与其他领域的联系，包括机器学习和并行计算，以及一些主要的开放性问题。在那地区。我们讨论的主题包括：AD的正向模式和反向模式，