Machine-learned reduced order modeling toward an effective flow control framework

Reduced order modeling is one of the promising techniques for designing efficient flow control schemes. However, mathematical derivation of a control law is still difficult if the low-dimensionalized dynamics is nonlinear. We propose a new machine-learned reduced order modeling to derive linear ordinary differential equations (ODE) that govern low-dimensionalized flow dynamics, named linear system extraction autoencoder (LEAE). The LEAE consists of a convolutional neural network-based autoencoder (CNN-AE) and an additional layer in its bottleneck. The CNN-AE has ever been utilized to efficiently map a high-dimensional phenomena into a low-dimensional latent space, and here we also employ the additional layer named linear ODE (LODE) layer to seek a governing equation of the latent dynamics in a form of linear ODE. Inside the LODE layer, a time integration scheme of the ODE for one time step is emulated, and the coefficient matrix is optimized through the training process with temporally consecutive latent vectors. It should be emphasized that the CNN-AE and the LODE layer are trained simultaneously such that the latent dynamics are governed by a system of linear ODE. This LEAE can successfully reproduce the two-dimensional cylinder wake at Re_D = 100 as an example of high-dimensional flow data. In the talk, we will show statistical assessments and applications to cases with blowing/suction control.