标题： 瑞利-贝纳德对流的控制：强化学习在湍流状态下的有效性 显示英文标题

标题： Control of Rayleigh-Bénard Convection: Effectiveness of Reinforcement Learning in the Turbulent Regime

摘要： 数据驱动的流动控制在工业、能源系统和气候科学领域具有巨大的潜力。本研究研究了强化学习 (RL) 在湍流不断增强的二维瑞利-伯纳德对流 (RBC) 系统中减少对流传热的有效性。我们研究了控制在不同初始条件和湍流程度下的泛化能力，并引入了一种奖励塑造技术来加速训练。将通过单智能体近端策略优化 (PPO) 训练的 RL 智能体与经典控制理论中的线性比例微分 (PD) 控制器进行了比较。RL 智能体在中等湍流系统中将对流（以努塞尔特数衡量）降低了高达 33%，在高湍流设置中降低了 10%，在所有设置中均明显优于 PD 控制。智能体在不同初始条件下表现出强大的泛化性能，并且在更高程度的湍流中也具有显著的泛化能力。奖励塑造提高了样本效率，并持续稳定了努塞尔特数在更高的湍流水平。 显示英文摘要

摘要： Data-driven flow control has significant potential for industry, energy systems, and climate science. In this work, we study the effectiveness of Reinforcement Learning (RL) for reducing convective heat transfer in the 2D Rayleigh-B\'enard Convection (RBC) system under increasing turbulence. We investigate the generalizability of control across varying initial conditions and turbulence levels and introduce a reward shaping technique to accelerate the training. RL agents trained via single-agent Proximal Policy Optimization (PPO) are compared to linear proportional derivative (PD) controllers from classical control theory. The RL agents reduced convection, measured by the Nusselt Number, by up to 33% in moderately turbulent systems and 10% in highly turbulent settings, clearly outperforming PD control in all settings. The agents showed strong generalization performance across different initial conditions and to a significant extent, generalized to higher degrees of turbulence. The reward shaping improved sample efficiency and consistently stabilized the Nusselt Number to higher turbulence levels.