Lossy compression techniques supporting unsteady adjoint on 2D/3D unstructured grids

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. (C) 2021 Elsevier B.V. All rights reserved.