Deep-learning assisted reduced order model for high-dimensional flow prediction from sparse data

The reconstruction and prediction of full-state flows from sparse data are of great scientific and engineering significance yet remain challenging, especially in applications where data are sparse and/or subjected to noise. To this end, this study proposes a deep-learning assisted non-intrusive reduced order model (named DCDMD) for high-dimensional flow prediction from sparse data. Based on the compressed sensing (CS)-dynamic mode decomposition (DMD), the DCDMD model is distinguished by two novelties. First, a sparse matrix is defined to overcome the strict random distribution condition of sensor locations in CS, thus allowing flexible sensor deployments and requiring very few sensors. Second, a deep-learning-based proxy is invoked to acquire coherent flow modes from the sparse data of high-dimensional flows, thereby addressing the issue of defining sparsity and the stringent incoherence condition in the conventional CSDMD. The two advantageous features, combined with the fact that the model retains flow physics in the online stage, lead to significant enhancements in accuracy and efficiency, as well as superior insensitivity to data noises (i.e., robustness), in both reconstruction and prediction of full-state flows. These are demonstrated by three benchmark examples, i.e., cylinder wake, weekly mean sea surface temperature, and isotropic turbulence in a periodic square area.