Generalization Capability of Deep Learning for Predicting Drag Reduction in Pulsating Turbulent Pipe Flow with Arbitrary Acceleration and Deceleration
The spatiotemporal evolution of pulsating turbulent pipe flow was predicted by deep learning. A convolutional neural network (CNN) and long short-term memory (LSTM) were employed for long-term prediction by recursively predicting the local temporal evolution. To enhance prediction, physical components such as wall shear stress were informed into the training process. The datasets were obtained from direct numerical simulation (DNS). The model was trained exclusively on a limited set of sinusoidal pulsating flows driven by pressure gradients defined by their period and amplitude. Subsequently, 36 pulsating flows with arbitrary non-sinusoidal acceleration and deceleration were predicted to evaluate the generalization capability, defined as the predictive performance on unseen data during training. The model successfully predicted drag reduction rates ranging from $-1\%$ to $86\%$, with a mean absolute error of 9.2. This predictive performance for unseen pulsations indicates that local temporal prediction plays a central role, rather than learning the global profile of the pulsating waveforms. This implication was quantitatively verified by analyzing the differences in periodic $C_f$--$Re_b$ trajectories between the training and test datasets, demonstrating that flows exhibiting local similarity to the training data are more predictable. Furthermore, it was demonstrated that flows exhibiting intermittent laminar--turbulent transition and relaminarization become predictable when such regimes are incorporated into the training data. The results indicate that accurate prediction is achievable provided that the training data sufficiently cover the local flow-state space, highlighting the importance of appropriate training data selection for generalized flow prediction.