Postdoc: Parallelism & Procatical Application of Automatic Differentiation

该研究计划将自动微分（AD）和并行计算相结合，针对工程中的大规模反问题。 AD涉及精确导数的计算，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海森矩阵的有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是不切实际的，这主要是由于过多的内存需求。 通常，逆问题属于这一类。 该研究计划的重点是在并行计算环境中的工程反问题的梯度的高效自动生成。 反向模式原则上对于计算梯度向量是最佳有效的;然而，在实践中，存储器要求（以及随后的交换等）是有问题的 PI将在并行计算环境中开发AD方法，其中可用内存更大。 此外，他们将研究使用递归检查点技术来大大减少内存需求。

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.