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Mathematical modeling is applied to study phenomena and system behavior.In various engineering fields, many physical phenomena are illustrated using a set of differential equations.In many real-world applications, the mathematical models are very complex, and numerical simulations in high-dimensional systems are challenging.Examples of these problems are large-scale physical problems such as geophysical, which have high temporal and spatial variations.In these problems, model order reduction is a useful method for achieving an appropriate approximation because it can significantly decrease computational costs.Deep learning has recently been used to explore information from data and make predictions.There are several methods for dimensionality reduction.In this paper, we combine the dynamic mode decomposition (DMD) and the long short-term memory (LSTM) network.This is because LSTM can predict nonlinear systems and time series data.We use LSTM and DMD to predict nonlinear systems and reduce dimensions, respectively.Four common DMD schemes have been applied for dimensionality reduction.The common geophysical dataset has been used to evaluate the performance of the proposed method.Finally, we compare the variations of the modal coefficients which are obtained from snapshots projection and the reduced-order model.These results show the high accuracy of our proposed method.One of the things that is important is the time complexity of algorithm implementation.The time complexity of the proposed method is 10 times faster when 15 modes are used for modeling than when all features are used.

A surrogate non-intrusive reduced order model of quasi-geostrophic turbulence dynamics based on a combination of LSTM and different approaches of DMD