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There is a critical need for efficient and reliable active flow controlstrategies to reduce drag and noise in aerospace and marine engineeringapplications. While traditional full-order models based on the Navier-Stokesequations are not feasible, advanced model reduction techniques can beinefficient for active control tasks, especially with strong non-linearity andconvection-dominated phenomena. Using convolutional recurrent autoencodernetwork architectures, deep learning-based reduced-order models have beenrecently shown to be effective while performing several orders of magnitudefaster than full-order simulations. However, these models encounter significantchallenges outside the training data, limiting their effectiveness for activecontrol and optimization tasks. In this study, we aim to improve theextrapolation capability by modifying network architecture and integratingcoupled space-time physics as an implicit bias. Reduced-order models via deeplearning generally employ decoupling in spatial and temporal dimensions, whichcan introduce modeling and approximation errors. To alleviate these errors, wepropose a novel technique for learning coupled spatial-temporal correlationusing a 3D convolution network. We assess the proposed technique against astandard encoder-propagator-decoder model and demonstrate a superiorextrapolation performance. To demonstrate the effectiveness of 3D convolutionnetwork, we consider a benchmark problem of the flow past a circular cylinderat laminar flow conditions and use the spatio-temporal snapshots from thefull-order simulations. Our proposed 3D convolution architecture accuratelycaptures the velocity and pressure fields for varying Reynolds numbers.Compared to the standard encoder-propagator-decoder network, thespatio-temporal-based 3D convolution network improves the prediction range ofReynolds numbers outside of the training data.

Combined space-time reduced-order model with 3D deep convolution for extrapolating fluid dynamics