Machine-learning based flow field estimation using floating sensor locations

Based on machine learning techniques, we propose a novel method to estimate flow fields using only floating sensor locations. This method does not require either ground-truth velocity fields or governing equations for fluid flows, which is attractive for practical applications. The machine learning model is supposed to generate accurate velocity fields so that the time variation of sensor motion is consistent with the given data of sensor locations. To validate the method, the estimation accuracy, the dependence on the number of sensors, the time intervals for the sensor location data, and the robustness to noise are investigated using three examples of two-dimensional flows: the flow around a circular cylinder, the forced homogeneous isotropic turbulence, and the ocean currents. These investigations demonstrate the performance and practicality of this method, revealing that the accuracy can be comparable to the state-of-the-art physics-informed neural networks (PINNs)-based method even without any assumption of governing equations. Moreover, we observe that the present method can estimate the major structures, such as periodic wakes behind a cylinder, coherent structures in the forced turbulence, and stable ocean currents, with only a few sensors. We believe the present method can provide effective utilization of floating sensor observations in various fields.