论文标题
与时间相关的PDE和规范约束的强大的，离散的梯度下降程序，用于优化
A robust, discrete-gradient descent procedure for optimisation with time-dependent PDE and norm constraints
论文作者
论文摘要
流体动力学中的许多物理问题可以从规范约束优化问题角度重铸；在球形歧管上无限制的问题可以进一步重铸。由于管理PDE的非线性以及对此类系统进行最佳控制的计算成本，改善优化过程的数值收敛性至关重要。借用在流形社区的优化中借用工具，我们概述了直接参与循环方法的数值一致，离散的配方，并伴随着梯度下降和具有全局融合保证的线路搜索算法。我们在数值上证明了该公式在流体动力学中相关的三个示例问题上的鲁棒性，并提供了一个随附的库SpherManopt
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing PDEs, and the computational cost of performing optimal control on such systems, improving the numerical convergence of the optimisation procedure is crucial. Borrowing tools from the optimisation on manifolds community we outline a numerically consistent, discrete formulation of the direct-adjoint looping method accompanied by gradient descent and line-search algorithms with global convergence guarantees. We numerically demonstrate the robustness of this formulation on three example problems of relevance in fluid dynamics and provide an accompanying library SphereManOpt
