Development of a Reduced Order Model of Geostrophic Flow based on Combination of POD and Long-Short Term Memory Network

Mathematical modeling is used to study the phenomena and behavior of the system. Complex mathematical equations require powerful and time-consuming computational tools where they must be examined in order to obtain the correct behavior of a system.. In various science and engineering fields, many physical phenomena are introduced using a set of differential equations. They are known as mathematical models of physical systems. High-accuracy numerical simulations utilize numerical schemes and modeling tools to solve this set of equations and generate useful information about the behavior of a system. However, software engineering and processor technologies are rapidly advancing; computational complication is still an important factor in the simulation with high accuracy. It makes many restrictions in the solution of scientific problems in different research fields. Some examples of these problems are large-scale physical problems such as geophysical and atmospheric flows, which have high temporal and spatial variations. Therefore, the development of effective and robust algorithms to achieve the maximum quality of numerical simulations with the optimal computational cost is a research topic. There are several methods for dimension reduction but this study used a combination of POD and long short term memory (LSTM) network. Finally, comparing the results related to the modal coefficients which are obtained by the reduced-order model and CFD snapshots projection shows the high accuracy of the proposed method.