We propose a method using supervised machine learning to estimate velocity fields from particle images having missing regions due to experimental limitations. As a first example, a velocity field around a square cylinder at the Reynolds number of Re D = 300 is considered. To train machine learning models, we utilize artificial particle images (APIs) as the input data, which mimic the images of the particle image velocimetry (PIV). The output data are the velocity fields, and the correct answers for them are given by a direct numerical simulation (DNS). We examine two types of the input data: APIs without missing regions (i.e., full APIs) and APIs with missing regions (lacked APIs). The missing regions in the lacked APIs are assumed following the exact experimental situation in our wind tunnel setup. The velocity fields estimated from both full and lacked APIs are in great agreement with the reference DNS data in terms of various statistical assessments. We further apply these machine learned models trained with the DNS data to experimental particle images so that their applicability to the exact experimental situation can be investigated. The velocity fields estimated by the machine learned models contain approximately 40 fold denser data than that with the conventional cross-correlation method. This finding suggests that we may be able to obtain finer and hidden structures of the flow field, which cannot be resolved with the conventional cross-correlation method. We also find that even the complex flow structures are hidden due to the alignment of two square cylinders, the machine learned model is able to estimate the field in the missing region reasonably well. The present results indicate a great potential of the proposed machine learning-based method as a new data reconstruction method for PIV.
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