Design of Observers for the Flow around a Cylinder using Machine Learning Techniques

To estimate quantities of a flow field online, the computational cost of observers must be reduced. In this paper, we propose a method for designing computationally inexpensive observers for fluid flows with the aid of machine learning techniques. In the proposed method, an observer is first designed for a full-order model for the fluid flow, and the input/output data of the observer are obtained in the numerical simulation. Next, an observer imitating the original observer is extracted from these input/output data by using machine learning techniques. As a benchmark problem, we design observers for the flow around a cylinder with the proposed method. By using linear system identification and Gaussian process regression, two observers were extracted from the input/output data of the ensemble Kalman filter (EnKF) which is designed based on a full-order model. The numerical simulations revealed that the velocity distribution around the cylinder was successfully estimated from the surface pressure by the extracted observers in a short computation time. In particular, the observer extracted by Gaussian process regression showed almost the same estimation accuracy as the full-order EnKF.