In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy that mitigates gradient imbalance through incorporating adaptive weights in conjunction with dynamically adjusting learning rate is used during the training process to improve the convergence of PINNs. The performance of PINNs is assessed here by solving both the forward and inverse problems. In the forward problem, by encapsulating the physical relations among relevant variables, PINNs demonstrate their effectiveness in accurately forecasting the compressor's flow field. PINNs also show obvious advantages over the traditional CFD approaches, particularly in scenarios lacking complete boundary conditions, as is often the case in inverse engineering problems. PINNs successfully reconstruct the flow field of the compressor cascade solely based on partial velocity vectors and near-wall pressure information. Furthermore, PINNs show robust performance in the environment of various levels of aleatory uncertainties stemming from labeled data. This research provides evidence that PINNs can offer turbomachinery designers an additional and promising option alongside the current dominant CFD methods.

翻译：本研究首次将新兴的物理信息神经网络(PINNs)方法应用于压气机叶栅流场预测。区别于传统训练方式，本工作采用新型自适应学习策略，通过结合自适应权重与动态调整学习率缓解梯度失衡问题，从而在训练过程中改善PINNs的收敛性能。本文通过求解正问题与反问题评估PINNs的表现。在正问题求解中，通过封装相关变量间的物理关系，PINNs展现出准确预测压气机流场的有效性。尤其在反工程问题中常出现的边界条件不完备场景下，PINNs相较于传统CFD方法具有显著优势：仅基于部分速度矢量与近壁面压力信息，PINNs即可成功重构压气机叶栅流场。此外，PINNs在标注数据存在不同程度偶然不确定性时仍展现出稳健性能。本研究为透平机械设计人员提供了证据，证明在当前主流的CFD方法之外，PINNs可成为一项具有前景的补充工具。