Inferring Unsteady Wake Flow Fields From Partial Data by Physics-Informed Neural Networks

Abstract Massive differential numerical computations are necessary in Computational Fluid Dynamics. In addition, the experimental results are generally noisy. Consequently, traditional methods cannot get unsteady flow fields immediately and precisely. In this research, the inferences of unsteady wake flow fields at different Reynolds numbers by Physics-Informed Neural Networks (PINNs) are studied. Unlike typical neural networks whose loss function consists of Mean Square Error only, the loss function of PINNs consists of Mean Square Error and the sum of squares of residuals of the flow governing equations. The flow governing equations are introduced to the neural networks as a regularization of the loss function. The existence of regular term reduces the dependence on labeled data during training. Then the PINNs is trained with very little labeled data (5% of the full field). After being trained, the PINNs show excellent performance in inferring the unsteady wake flow fields. When the Reynolds number is 1e2, the Mean Absolute Error (MAE) of the reconstructed velocity field is on the order of 1e−4. Meanwhile, the MAE increases with the increase of Reynolds number. In addition, even if the random noise of the training set is introduced up to 20%, the result is still acceptable, which demonstrates the great anti-noise ability of physics-informed neural networks.