基于软件的自动区分是有缺陷的

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics Pub Date : 2025-09-02 DOI:10.1016/j.jcp.2025.114319

Daniel Johnson , Trevor Maxfield , Yongxu Jin , Ronald Fedkiw

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引用次数: 0

摘要

自动微分中的软件工作是建立在这样的观察基础上的：每个计算都是作为一系列基本操作实现的，并且可以为每个这些操作提供符号偏导数。然后可以利用链式法则来累加导数来遍历任何计算（向前或向后）。这些框架没有在求值之前简化这些表达式的机制。如下所示，所产生的错误往往是无界的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Software-based automatic differentiation is flawed

Software efforts in automatic differentiation are built on the observation that every computation is implemented as a series of elementary operations, and that symbolic partial derivatives can be supplied for each of these operations. Any computation can then be traversed (either forwards or backwards) utilizing the chain rule to accumulate derivatives. These frameworks have no mechanism for simplifying these expressions before evaluating them. As we illustrate below, the resulting errors tend to be unbounded.

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来源期刊

Journal of Computational Physics 物理-计算机：跨学科应用

CiteScore

7.60

自引率

14.60%

发文量

763

审稿时长

5.8 months

期刊介绍： Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.