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The reconstruction and prediction of full-state flows from sparse data are ofgreat scientific and engineering significance yet remain challenging,especially in applications where data are sparse and/or subjected to noise. Tothis end, this study proposes a deep-learning assisted non-intrusive reducedorder model (named DCDMD) for high-dimensional flow prediction from sparsedata. Based on the compressed sensing (CS)-Dynamic Mode Decomposition (DMD),the DCDMD model is distinguished by two novelties. Firstly, a sparse matrix isdefined to overcome the strict random distribution condition of sensorlocations in CS, thus allowing flexible sensor deployments and requiring veryfew sensors. Secondly, a deep-learning-based proxy is invoked to acquirecoherent flow modes from the sparse data of high-dimensional flows, therebyaddressing the issue of defining sparsity and the stringent incoherencecondition in the conventional CSDMD. The two advantageous features, combinedwith the fact that the model retains flow physics in the online stage, lead tosignificant enhancements in accuracy and efficiency, as well as superiorinsensitivity to data noises (i.e., robustness), in both reconstruction andprediction of full-state flows. These are demonstrated by three benchmarkexamples, i.e., cylinder wake, weekly-mean sea surface temperature andisotropic turbulence in a periodic square area.

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