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

Joogoo Jeon, Jean Rabault+4 more|arXiv (Cornell University)|Jul 25, 2024

Model Reduction and Neural Networks4 citations

TL;DR

This paper proposes a novel deep reinforcement learning (DRL) framework for flow control that integrates group-invariant neural networks (GI-NNs) and positional encoding within a multi-agent reinforcement learning (MARL) setup. By enforcing spatial symmetry invariance and injecting location-aware representations, the method accelerates learning speed by 50% and improves policy quality, reducing the Nusselt number by up to 15% in Rayleigh-Bénard convection simulations.

ABSTRACT

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-Bénard 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.

Motivation & Objective

• Address the limitations of traditional flow control in nonlinear, high-dimensional fluid systems.
• Overcome challenges in training deep reinforcement learning agents for complex fluid dynamics by incorporating inductive biases.
• Improve sample efficiency and policy performance in flow control via symmetry-aware and location-aware neural network architectures.
• Investigate the complementary roles of group invariance (for speed) and positional encoding (for quality) in DRL-based flow control.
• Demonstrate the method’s effectiveness on a canonical Rayleigh-Bénard convection benchmark with measurable improvements in convergence and performance.

Proposed method

• Employ multi-agent reinforcement learning (MARL) to exploit spatial policy invariance across fluid domains.
• Integrate group-invariant neural networks (GI-NNs) to enforce local symmetry invariance, ensuring equivariant representations under spatial transformations.
• Apply positional encoding inspired by the transformer architecture to inject spatial location information into the agent's observations.
• Combine GI-NNs and positional encoding in a shared DRL backbone to balance invariance and expressivity.
• Train the DRL agent using proximal policy optimization (PPO) with a reward shaped to minimize the Nusselt number.
• Use a 2D Rayleigh-Bénard convection setup as the environment, with finite-difference-based flow simulations for policy training.

Experimental results

Research questions

• RQ1 Can group-invariant neural networks improve the sample efficiency and convergence speed of DRL agents in fluid flow control?
• RQ2 To what extent does positional encoding enhance the policy quality and stability of DRL agents in high-dimensional flow systems?
• RQ3 How do group invariance and positional encoding interact in a multi-agent DRL framework for flow control?
• RQ4 Does the integration of symmetry and location-aware representations lead to more reproducible and robust learning outcomes?
• RQ5 Can the proposed method achieve lower Nusselt numbers compared to standard MARL baselines in Rayleigh-Bénard convection?

Key findings

• Group-invariant neural networks (GI-NNs) reduced DRL training time by approximately 50% compared to the base MARL baseline.
• The GI-NNs achieved better average policy performance, with a notable improvement in learning reproducibility.
• Positional encoding further reduced the minimum Nusselt number by up to 15% compared to the GI-NN baseline.
• The combination of GI-NNs and positional encoding stabilized convergence and improved robustness across multiple training runs.
• GI-NNs specialized in accelerating learning speed, while positional encoding specialized in enhancing policy quality and final performance.
• The results demonstrate that architectural inductive biases—specifically symmetry and location awareness—are critical for efficient and effective DRL in fluid dynamics.