A predictive hybrid reduced order model based on proper orthogonal decomposition combined with deep learning architectures

Solving computational fluid dynamics problems requires using large computational resources. The computational time and memory requirements to solve realistic problems vary from a few hours to several weeks with several processors working in parallel. Motivated by the need of reducing such large amount of resources (improving the industrial applications in which fluid dynamics plays a key role), this article introduces a new predictive Reduced Order Model (ROM) applied to solve fluid dynamics problems. The model is based on physical principles and combines modal decompositions with deep learning architectures. The hybrid ROM, reduces the dimensionality of a database via proper orthogonal decomposition (POD), extracting the dominant features leading the flow dynamics of the problem studied. The number of degrees of freedom are reduced from hundred thousands spatial points describing the database to a few (20-100) POD modes. Firstly, POD divides the spatio-temporal data into spatial modes and temporal coefficients (or temporal modes). Next, the temporal coefficients are integrated in time using convolutional or recurrent neural networks. The temporal evolution of the flow is approximated after combining the spatial modes with the new temporal coefficients computed. The model is tested in two complex problems of fluid dynamics, the three-dimensional wake of a circular cylinder and a synthetic jet. The hybrid ROM uses data from the initial transient stage of numerical simulations to predict the temporally converged solution of the flow with high accuracy. The speed-up factor comparing the time necessary to obtain the predicted solution using the hybrid ROM and the numerical solver is similar to 140-348 in the synthetic jet and similar to 2897-3818 in the three dimensional cylinder wake. The robustness shown in the results presented and the data-driven nature of this ROM, make it possible to extend its application to other fields (i.e. video and language processing, robotics, finances).