This paper proposes and assesses remedies to the significant storage requirements of unsteady adjoint methods used in gradient-based optimization, in multi-dimensional problems modeled by unsteady PDEs. Even if the application domain of the proposed technique(s) is wide, these remedies are herein demonstrated in shape optimization problems with unsteady fluid flows. In these cases, the adjoint equations are integrated backwards in time, requiring the instantaneous flow fields to be available at each time-step of the adjoint solver, and this noticeably increases storage requirements. To avoid extreme treatments, such as the full storage of the computed instantaneous flow fields or their recomputations from scratch during the solution of the adjoint equations, or even the widely used check-pointing technique, lossy compression techniques are proposed. These are implemented within OpenFOAM, which is used to solve the flow and adjoint equations and conduct the optimization. In this paper, (a) the ZFP compression library, (b) the incremental Proper Generalized Decomposition (iPGD) algorithm and (c) an efficient hybridization of them are used. The compression strategies are assessed on aerodynamic shape optimization problems. Their effectiveness in data reduction, computational overhead and representation accuracy is considered, in relation to the continuous adjoint method which uses the decompressed fields to compute the gradient of objective functions as the reference method.

本文提出并评估了对基于梯度的优化中使用的非稳态伴随方法的显着存储要求的补救措施，在非稳态 PDE 建模的多维问题中。即使所提出的技术的应用领域很广，这些补救措施在本文中在具有不稳定流体流动的形状优化问题中得到了证明。在这些情况下，伴随方程在时间上向后积分，要求瞬时流场在伴随求解器的每个时间步长可用，这显着增加了存储需求。避免极端处理，例如完全存储计算的瞬时流场或其重新计算在求解伴随方程的过程中，从头开始，甚至广泛使用的检查点技术，都提出了有损压缩技术。这些在 OpenFOAM 中实现，用于求解流动和伴随方程并进行优化。在本文中，(a) ZFP 压缩库，(b) 增量适当广义分解 (iPGD) 算法和 (c) 使用了它们的有效混合。在空气动力学形状优化问题上评估压缩策略。考虑到它们在数据缩减、计算开销和表示精度方面的有效性，与使用解压缩场计算目标函数梯度作为参考方法的连续伴随方法有关。