  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.
