Reduced order framework for convection dominant and pure diffusive problems based on combination of deep long short‐term memory and proper orthogonal decomposition/dynamic mode decomposition methods

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 article, a reduced order model framework based on a combination of deep learning [long short‐term memory (LSTM)] and proper orthogonal decomposition/dynamic mode decomposition (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 reduced order modeling (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 article is to 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.

Propulsion optimization of a jellyfish-inspired robot based on a nonintrusive reduced-order model with proper orthogonal decomposition

“…For example, the model reduction algorithm retains the main features of the solution state vector. Well-known methods for constructing reduced-order models (ROMs) include proper orthogonal decomposition (POD) [20][21][22], Koopman analysis [23] and dynamic mode decomposition [24][25][26][27].…”

Feasibility Analysis of a POD-Based Reduced Order Model with Application in Eulerian–Lagrangian Simulations

“…For the latter, reduced governing equations are replaced by a machine learning algorithm, for example, the radial basis function (RBF) 20,23,24 or the long−short-term memory (LSTM) neural network. 25,26 Up to now, most applications of the POD-based ROM have been concentrated in Eulerian simulations (e.g., refs 23,24). However, due to the complicated motion of solid particles, only a few studies explored POD's applications to Lagrangian systems.…”

“…In the nonintrusive ROM, Wu and Schaback derived the error bounds in the RBF interpolation method. Consistency error. In the ROM, a key underlying assumption is that the dominant POD modes in the training and testing data sets are essentially similar . When this assumption does not hold exactly, the inconsistent training problem for the testing data set would occur, thus triggering the consistency error.…”

“…For the former, the Galerkin projection is usually employed to derive the reduced governing equations. For the latter, reduced governing equations are replaced by a machine learning algorithm, for example, the radial basis function (RBF) ,, or the long–short-term memory (LSTM) neural network. , …”

Research on grid‐dependence of neural network turbulence model

“…With the rapid development of machine learning technology in recent years, remarkable breakthroughs have been made in speech recognition, computer vision and other fields. Inspired by this, researchers having been attempting to apply artificial intelligence (AI) to fluid mechanics, such as flow fields reconstruction, [3][4][5] aerodynamic force prediction, 6 and reduced-order models. [7][8][9] Machine learning has also been used for aerodynamic prediction and optimization of turbine rotor, 10 aerodynamic design, robustness optimization 11,12 and prediction of pressure distribution of airfoils.…”