Machine Learning-Based Three-Dimensional Reconstruction of Stress Field from Flow Birefringence

In biological fluid dynamics, measurement of the stress field in a blood flow is crucial for various applications, such as understanding the cause of cerebral aneurysms. However, since blood is a complex fluid, the constitutive equation for computing the stress field from the velocity field is still unclear. Therefore, we proposed a machine learning-based photoelasticity approach to measure the stress field of a complex fluid flow. Here, we show the results of the three-dimensional reconstruction of stress field from the measured flow birefringence. Numerical simulation was performed to obtain the data of the flow birefringence and stress fields of an axisymmetric pipe flow. The data is then used to train a deep convolutional encoder-decoder (DCED) model to predict the stress field from the flow birefringence. DCED achieved high accuracy in predicting the simulation data. Even for the experiment data, it has successfully predicted the trend of the stress distribution across the pipe's cross-section. The prediction can be improved by including the experiment data into the training data. The results obtained in this study indicate a major advance towards the non-contact stress measurement of a fluid flow, which will be an important tool to the field of biological fluid dynamics.