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Data I/O poses a significant bottleneck in large-scale CFD simulations; thus,practitioners would like to significantly reduce the number of times thesolution is saved to disk, yet retain the ability to recover any field quantity(at any time instance) a posteriori. The objective of this work is therefore toaccurately recover missing CFD data a posteriori at any time instance, giventhat the solution has been written to disk at only a relatively small number oftime instances. We consider in particular high-order discretizations (e.g.,discontinuous Galerkin), as such techniques are becoming increasingly popularfor the simulation of highly separated flows. To satisfy this objective, thiswork proposes a methodology consisting of two stages: 1) dimensionalityreduction and 2) dynamics learning. For dimensionality reduction, we propose anovel hierarchical approach. First, the method reduces the number of degrees offreedom within each element of the high-order discretization by applyingautoencoders from deep learning. Second, the methodology applies principalcomponent analysis to compress the global vector of encodings. This leads to alow-dimensional state, which associates with a nonlinear embedding of theoriginal CFD data. For dynamics learning, we propose to apply regressiontechniques (e.g., kernel methods) to learn the discrete-time velocitycharacterizing the time evolution of this low-dimensional state. A numericalexample on a large-scale CFD example characterized by nearly 13 million degreesof freedom illustrates the suitability of the proposed method in an industrialsetting.

Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning