Adjoint Methods Using POD State Reconstructions on Modern HPC Architectures
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Accessing the full time history of the state, either through direct storage or checkpointing and recomputation, can make adjoint sensitivity analysis of dynamical systems prohibitively costly over long time integration periods. This is particularly relevant in large scale Computational Fluid Dynamics (CFD) applications consisting of time averaged objective functions that may require long integration periods to converge. In this work we investigate integrating the adjoint system through a truncated reconstruction of the forward state based on a Proper Orthogonal Decomposition (POD). The forward and adjoint computations are performed using the GPU based spectral element solver Neko, meanwhile the POD computation is performed in-situ using the data processing toolbox pySEMTools. The POD algorithm is both parallel in space and streaming in time, enabling the use in large scale CFD applications. While similar methodologies have been explored in the past, a salient feature of the proposed method relates to modern HPC architectures consisting of both CPUs and GPUs. Performing the CFD simulation on the GPUs allows the otherwise idle CPUs to be leveraged in performing the POD computation, again, reducing the overall cost. The proposed methodology is compared to the conventional method of checkpointing both in terms of cost reduction and errors incurred at various levels of POD truncation.
