A practical approach to flow field reconstruction with sparse or incomplete data through physics informed neural network

High-resolution flow field reconstruction is prevalently recognized as a difficult task in the field of experimental fluid mechanics, since the measured data are usually sparse and incomplete in time and space. Specifically, due to the limitations of experimental equipment or measurement techniques, the expected data cannot be measured in some key areas. In this paper, a practical approach is proposed to reconstruct flow field with imperfect data based on the physics informed neural network (PINN), which integrates those known data with the physical principles. The wake flow past a circular cylinder is taken as the test case. Two kinds of the training set are investigated, one is the velocity data with different sparsity, and the other is the velocity data missing in different regions. To accelerate training convergence, the learning rate schedule is discussed, and the cosine annealing algorithm shows excellent performance. Results reveal that the proposed approach not only can reconstruct the true velocity field with high accuracy, but also can predict the pressure field precisely, even when the data sparsity reaches 1% or the core flow area data are truncated away. This study provides encouraging insights that the PINN can serve as a promising data assimilation method for experimental fluid mechanics.