# Invariant Control Strategies for Active Flow Control using Graph Neural Networks

arXiv: https://arxiv.org/abs/2503.22775 · HTML: https://mlsanity.com/paper/2503.22775/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL with diffusion and flow models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 28 Mar 2025.

## Placed in

- Deep reinforcement learning methods / [RL with diffusion and flow models](https://mlsanity.com/deeprl/rl-with-diffusion-and-flow-models/)

## Builds on (most cited first, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [Distributed Distributional Deterministic Policy Gradients](https://mlsanity.com/paper/1804.08617/) (2018)
- [Continuous Deep Q-Learning with Model-based Acceleration](https://mlsanity.com/paper/1603.00748/) (2016)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [Effective control of two-dimensional Rayleigh--B'enard convection: invariant multi-agent reinforcement learning is all you need](https://mlsanity.com/paper/2304.02370/) (2023)
- [Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning](https://mlsanity.com/paper/2301.10737/) (2023)
- [You May Not Need Ratio Clipping in PPO](https://mlsanity.com/paper/2202.00079/) (2022)
- [Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks](https://mlsanity.com/paper/2308.01602/) (2023)
- [Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations](https://mlsanity.com/paper/2206.11038/) (2022)
- [Flow Completion Network: Inferring the Fluid Dynamics from Incomplete Flow Information using Graph Neural Networks](https://mlsanity.com/paper/2205.04739/) (2022)
- [Predicting fluid-structure interaction with graph neural networks](https://mlsanity.com/paper/2210.04193/) (2022)
- [FLEXI: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws](https://mlsanity.com/paper/1910.02858/) (2019)
- [Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systems](https://mlsanity.com/paper/2205.06502/) (2022)
- [Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning](https://mlsanity.com/paper/2309.06260/) (2023)
- [Advanced deep-reinforcement-learning methods for flow control: group-invariant and positional-encoding networks improve learning speed and quality](https://mlsanity.com/paper/2407.17822/) (2024)
- [Model-based deep reinforcement learning for accelerated learning from flow simulations](https://mlsanity.com/paper/2402.16543/) (2024)
- [Gym-preCICE: Reinforcement Learning Environments for Active Flow Control](https://mlsanity.com/paper/2305.02033/) (2023)
- [An Efficient Sliding Mesh Interface Method for High-Order Discontinuous Galerkin Schemes](https://mlsanity.com/paper/2008.04356/) (2020)
- [GALAEXI: Solving complex compressible flows with high-order discontinuous Galerkin methods on accelerator-based systems](https://mlsanity.com/paper/2404.12703/) (2024)

## Built on by (most cited first, 1 of 1)

- [Timescale Separation Enables Deep Reinforcement Learning Control of Rotating Detonation Engine Mode Transitions](https://mlsanity.com/paper/2604.14398/) (2026)

## Abstract (arXiv)

Reinforcement learning has gained traction for active flow control tasks, with initial applications exploring drag mitigation via flow field augmentation around a two-dimensional cylinder. RL has since been extended to more complex turbulent flows and has shown significant potential in learning complex control strategies. However, such applications remain computationally challenging due to its sample inefficiency and associated simulation costs. This fact is worsened by the lack of generalization capabilities of these trained policy networks, often being implicitly tied to the input configurations of their training conditions. In this work, we propose the use of graph neural networks to address this particular limitation, effectively increasing the range of applicability and getting more value out of the upfront RL training cost. GNNs can naturally process unstructured, threedimensional flow data, preserving spatial relationships without the constraints of a Cartesian grid. Additionally, they incorporate rotational, reflectional, and permutation invariance into the learned control policies, thus improving generalization and thereby removing the shortcomings of commonly used CNN or MLP architectures. To demonstrate the effectiveness of this approach, we revisit the well-established two-dimensional cylinder benchmark problem for active flow control. The RL training is implemented using Relexi, a high-performance RL framework, with flow simulations conducted in parallel using the high-order discontinuous Galerkin framework FLEXI. Our results show that GNN-based control policies achieve comparable performance to existing methods while benefiting from improved generalization properties. This work establishes GNNs as a promising architecture for RL-based flow control and highlights the capabilities of Relexi and FLEXI for large-scale RL applications in fluid dynamics.