Efficient Active Flow Control Strategy for Confined Square Cylinder Wake Using Deep Learning-Based Surrogate Model and Reinforcement Learning

This study presents a deep learning model-based reinforcement learning (DL-MBRL) approach for active control of two-dimensional (2D) wake flow past a square cylinder using antiphase jets. The DL-MBRL framework alternates between interacting with a deep learning surrogate model (DL-SM) and computational fluid dynamics (CFD) simulations to suppress wake vortex shedding, significantly reducing computational costs. The DL-SM, which combines a Transformer and a multiscale enhanced super-resolution generative adversarial network (MS-ESRGAN), effectively models complex flow dynamics, efficiently emulating the CFD environment. Trained on 2D direct numerical simulation (DNS) data, the Transformer and MS-ESRGAN demonstrated excellent agreement with DNS results, validating the DL-SM's accuracy. Error analysis suggests replacing the DL-SM with CFD every five interactions to maintain reliability. While DL-MBRL showed less robust convergence than model-free reinforcement learning (MFRL) during training, it reduced training time by 49.2%, from 41.87 hours to 20.62 hours. Both MFRL and DL-MBRL achieved a 98% reduction in shedding energy and a 95% reduction in the standard deviation of the lift coefficient (C_L). However, MFRL exhibited a nonzero mean lift coefficient due to insufficient exploration, whereas DL-MBRL improved exploration by leveraging the randomness of the DL-SM, resolving the nonzero mean C_L issue. This study demonstrates that DL-MBRL is not only comparably effective but also superior to MFRL in flow stabilization, with significantly reduced training time, highlighting the potential of combining deep reinforcement learning with DL-SM for enhanced active flow control.