Postdoc: Parallelism & Procatical Application of Automatic Differentiation

博士后：并行性

• 批准号: 9704685
• 负责人: Thomas Coleman
• 金额: $ 4.62万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-05-01 至 1999-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704685&HistoricalAwards=false
• 关键词: Postdoc; Parallelism; & Procatical; Application

The proposed research plan combines automatic differentiation (AD) and parallel computing, targeted toward large-scale inverse problems in engineering. AD is concerned with the computation of exact derivatives, up to an arbitrary order. Recent AD software packages are just beginning to bring the practical benefits of AD into the mainstream of computational science. Nevertheless, despite significant progress on the efficient computation of sparse Jacobiian and Hessian matrices, the reverse mode of AD remains impractical for large-scale problems involving dense derivative matrices, primarily due to excessive memory demands. Typically, inverse problems are in this category. The research plan is focused on the efficient automatic generation of gradients for inverse problems in engineering in a parallel computing setting. Reverse mode is in principle optimally efficient for computing gradient vectors; however in practice the memory requirements (and subsequent swapping, etc.) are problematic. The PI's will develop the AD methodology in the parallel computing setting, where the available memory is much greater. Moreover, they will investigate the use of the technique known as recursive checkpointing to greatly reduce memory requirements.

提出的研究方案将自动微分（AD）与并行计算相结合，针对工程中的大规模逆问题。AD关注的是精确导数的计算，直到任意阶。最近的AD软件包才刚刚开始将AD的实际好处带入计算科学的主流。然而，尽管在稀疏雅可比矩阵和Hessian矩阵的高效计算方面取得了重大进展，但AD的反向模式对于涉及密集导数矩阵的大规模问题仍然不切实际，这主要是由于过度的内存需求。通常，逆问题属于这一类。在并行计算环境下，研究工程反问题中梯度的高效自动生成问题。反向模式原则上是计算梯度向量的最优效率；然而，在实践中，内存需求（以及随后的交换等）是有问题的。PI将在并行计算设置中开发AD方法，其中可用内存要大得多。此外，他们还将研究递归检查点技术的使用，以大大减少内存需求。