Mahdi Kherad, Mohammad Kazem Moayyedi, Faranak Fotouhi
International Journal of Numerical Methods in Fluids, 2020
Abstract
In many real‐world applications, mathematical models are highly complex, and numerical simulations in high‐dimensional systems are challenging. Model order reduction is a useful method to obtain a reasonable approximation by significantly reducing the computational cost of such problems. Deep learning technology is a recent improvement in artificial neural networks that can find more hidden information from the data. Deep learning has the advantage of processing data in its raw form and trains the nonlinear system with different levels of representation and predicts the data. In this paper, a Reduced Order Model Framework Based on a combination of Deep Learning (LSTM) and POD/DMD Modes is presented. Due to the robustness and stability of the LSTM recurrent neural network in predicting chaotic dynamical systems, we consider LSTM architecture to develop our data‐driven ROM. We investigate the proposed method performance by solving two well‐known canonical cases: a steady shear flow exhibiting the Kelvin–Helmholtz instability, and Two‐dimensional and Unsteady Mass Diffusion Equation. The focus of this paper, use LSTM deep recursive neural network to learn the time dynamics and POD/DMD to generate the order reduction model. The results show that the proposed method is very accurate in predicting time dynamics and input reconstruction.