Advanced deep-reinforcement-learning methods for flow control: group-invariant and positional-encoding networks improve learning speed and quality

Flow control is key to maximize energy efficiency in a wide range of applications. However, traditional flow-control methods face significant challenges in addressing non-linear systems and high-dimensional data, limiting their application in realistic energy systems. This study advances deep-reinforcement-learning (DRL) methods for flow control, particularly focusing on integrating group-invariant networks and positional encoding into DRL architectures. Our methods leverage multi-agent reinforcement learning (MARL) to exploit policy invariance in space, in combination with group-invariant networks to ensure local symmetry invariance. Additionally, a positional encoding inspired by the transformer architecture is incorporated to provide location information to the agents, mitigating action constraints from strict invariance. The proposed methods are verified using a case study of Rayleigh-B\'enard convection, where the goal is to minimize the Nusselt number Nu. The group-invariant neural networks (GI-NNs) show faster convergence compared to the base MARL, achieving better average policy performance. The GI-NNs not only cut DRL training time in half but also notably enhance learning reproducibility. Positional encoding further enhances these results, effectively reducing the minimum Nu and stabilizing convergence. Interestingly, group invariant networks specialize in improving learning speed and positional encoding specializes in improving learning quality. These results demonstrate that choosing a suitable feature-representation method according to the purpose as well as the characteristics of each control problem is essential. We believe that the results of this study will not only inspire novel DRL methods with invariant and unique representations, but also provide useful insights for industrial applications.

Effective control of two-dimensional Rayleigh--Bénard convection: invariant multi-agent reinforcement learning is all you need

Rayleigh-B\'enard convection (RBC) is a recurrent phenomenon in several industrial and geoscience flows and a well-studied system from a fundamental fluid-mechanics viewpoint. However, controlling RBC, for example by modulating the spatial distribution of the bottom-plate heating in the canonical RBC configuration, remains a challenging topic for classical control-theory methods. In the present work, we apply deep reinforcement learning (DRL) for controlling RBC. We show that effective RBC control can be obtained by leveraging invariant multi-agent reinforcement learning (MARL), which takes advantage of the locality and translational invariance inherent to RBC flows inside wide channels. The MARL framework applied to RBC allows for an increase in the number of control segments without encountering the curse of dimensionality that would result from a naive increase in the DRL action-size dimension. This is made possible by the MARL ability for re-using the knowledge generated in different parts of the RBC domain. We show in a case study that MARL DRL is able to discover an advanced control strategy that destabilizes the spontaneous RBC double-cell pattern, changes the topology of RBC by coalescing adjacent convection cells, and actively controls the resulting coalesced cell to bring it to a new stable configuration. This modified flow configuration results in reduced convective heat transfer, which is beneficial in several industrial processes. Therefore, our work both shows the potential of MARL DRL for controlling large RBC systems, as well as demonstrates the possibility for DRL to discover strategies that move the RBC configuration between different topological configurations, yielding desirable heat-transfer characteristics. These results are useful for both gaining further understanding of the intrinsic properties of RBC, as well as for developing industrial applications.