This paper presents a novel model reduction method: deep learning reduced order model, which is based on proper orthogonal decomposition and deep learning methods. The deep learning approach is a recent technological advancement in the field of artificial neural networks. It has the advantage of learning the nonlinear system with multiple levels of representation and predicting data. In this work, the training data are obtained from high fidelity model solutions at selected time levels. The long short-term memory network is used to construct a set of hypersurfaces representing the reduced fluid dynamic system. The model reduction method developed here is independent of the source code of the full physical system.

The reduced order model based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new reduced order model is evaluated using 2 numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.