Prediction of subsonic cascade flow fields by physics-informed graph neural networks with unbalanced data

Abstract

Accurate and fast prediction of flow field is a significant task for compressor design and optimization which leads to a faster iteration of design cycle. Deep learning method shows ability to solve diverse types of problem and has enormous potential in flow field reconstruction. Graph neural networks (GNN) is one of verified structures of deep learning model and is well-suited for the flow field prediction task. Data of compressor is usually insufficient or unbalanced since the high cost of experiment or high-fidelity simulation and leads to the deterioration of deep learning model. To improve the deep learning model performance with unbalanced training data, a physic-informed graph neural networks (PIGNN) model is suggested with the residual of governing equations introduced into the loss function to constraint the prediction of flow field. As a typical case, the cascade flow field is selected to be the research object in this study. The residual of governing equations is fast calculated in batch by numerical differential. With the guidance of physics-informed learning, PIGNN outperforms GNN in flow field prediction while its mean error decreases 13.4 % with balanced data and up to 38.6 % with different unbalanced data. The model performances at different inlet conditions and the predictions of key characteristics are explored simultaneously. The mean prediction error of key characteristics is reduced over 10 % in most situations by physics-informed learning.