Distributed control of Rayleigh-Bénard convection using symmetry exploiting deep reinforcement learning
(Codebase will be public soon...)
| Uncontrolled case | Controlling via multi-agents |
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(click on the thumbnails to see the video :-))
We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs). Exploiting translational equivariances, the high-dimensional distributed control problem can be transformed into a multi-agent control problem with many identical, uncoupled agents. Furthermore, using the fact that information is transported with finite velocity in many cases, the dimension of the agents’ environment can be drastically reduced using a convolution operation over the state space of the PDE, by which we effectively tackle the curse of dimensionality otherwise present in deep reinforcement learning. In this setting, the complexity can be flexibly adjusted via the kernel width or by using a stride greater than one (meaning that we do not place an actuator at each sensor location). Moreover, scaling from smaller to larger domains – or the transfer between different domains – becomes a straightforward task requiring little effort. We use our framework to study a particularly challenging and relevant PDE system, namely Rayleigh–Bénard convection. Employing low-dimensional proximal policy optimisation (PPO) agents, we effectively reduce the Nusselt number of the system, which is a measure of convective heat transfer. Furthermore, we show the agents trained in such a paradigm generalizes well not only to longer time horizons, but also to increasingly chaotic flow regimes characterised by Rayleigh number (Ra) with little or no retraining.