Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade with the primary goal to decompose complex flows to a set of features most important for future state prediction and control, typically using a dimensionality reduction technique. In this work, a novel data-driven technique based on the power of deep neural networks for reduced order modeling of the unsteady fluid flows is introduced. An autoencoder network is used for nonlinear dimension reduction and feature extraction as an alternative for singular value decomposition (SVD). Then, the extracted features are used as an input for long short-term memory network (LSTM) to predict the velocity field at future time instances. The proposed autoencoder-LSTM method is compared with dynamic mode decomposition (DMD) as the data-driven base method. Moreover, an autoencoder-DMD algorithm is introduced for reduced order modeling, which uses the autoencoder network for dimensionality reduction rather than SVD rank truncation. Results show that the autoencoder-LSTM method is considerably capable of predicting the fluid flow evolution, where higher values for coefficient of determination $R^{2}$ are obtained using autoencoder-LSTM comparing to DMD.
翻译:不稳定的流体系统是非线性高维动态系统,在时间和空间上都可能出现多种复杂现象。减少流体流的顺序建模(ROM)是近十年来一个积极的研究课题,其主要目标是将复杂的流分解成对未来国家预测和控制最重要的一系列特征,通常使用一个维度减少技术。在这项工作中,采用了基于深神经网络的力量的新型数据驱动技术,以减少不稳定的流体流的顺序建模。引入了自动解码器网络,用于非线性规模的减少和特征提取,作为单值分解(SVD)的替代品。随后,将提取的特征用作长期短期内存网络(LSTM)的一个投入,用于预测未来时间的速度场。拟议的自动解析器-LSTM方法与数据驱动的动态模式解剖法(DMD)进行了比较。此外,引入了自动解码器-DMD算法,用于减少排序,使用自动解算器网络进行单值递减缩,而不是进行SVDLS的自动解算法。