Multi-agent Reinforcement Learning for the Control of Three-Dimensional Rayleigh–Bénard Convection
Joel Vasanth, Jean Rabault, Francisco Alcántara-Ávila, Mikael Mortensen, Ricardo Vinuesa
Abstract
Abstract Deep reinforcement learning (DRL) has found application in numerous use-cases pertaining to flow control. Multi-agent RL (MARL), a variant of DRL, has shown to be more effective than single-agent RL in controlling flows exhibiting locality and translational invariance. We present, for the first time, an implementation of MARL-based control of three-dimensional Rayleigh–Bénard convection (RBC). Control is executed by modifying the temperature distribution along the bottom wall divided into multiple control segments, each of which acts as an independent agent. Two regimes of RBC are considered at Rayleigh numbers $$\textrm{Ra}=500$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>Ra</mml:mtext> <mml:mo>=</mml:mo> <mml:mn>500</mml:mn> </mml:mrow> </mml:math> and 750. Evaluation of the learned control policy reveals a reduction in convection intensity by $$23.5\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>23.5</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> and $$8.7\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>8.7</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> at $$\textrm{Ra}=500$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>Ra</mml:mtext> <mml:mo>=</mml:mo> <mml:mn>500</mml:mn> </mml:mrow> </mml:math> and 750, respectively. The MARL controller converts irregularly shaped convective patterns to regular straight rolls with lower convection that resemble flow in a relatively more stable regime. We draw comparisons with proportional control at both $$\textrm{Ra}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>Ra</mml:mtext> </mml:math> and show that MARL is able to outperform the proportional controller. The learned control strategy is complex, featuring different non-linear segment-wise actuator delays and actuation magnitudes. We also perform successful evaluations on a larger domain than used for training, demonstrating that the invariant property of MARL allows direct transfer of the learnt policy.