# A reinforcement learning strategy to automate and accelerate h/p-multigrid solvers

arXiv: https://arxiv.org/abs/2407.15872 · HTML: https://mlsanity.com/paper/2407.15872/

## Key facts

- Cited by 2 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 7 of its 40 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## 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, 7 of 7)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [A review on Deep Reinforcement Learning for Fluid Mechanics](https://mlsanity.com/paper/1908.04127/) (2019)
- [Direct shape optimization through deep reinforcement learning](https://mlsanity.com/paper/1908.09885/) (2019)
- [Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning](https://mlsanity.com/paper/2309.06260/) (2023)
- [A reinforcement learning strategy for p-adaptation in high order solvers](https://mlsanity.com/paper/2306.08292/) (2023)
- [p-Multigrid matrix-free discontinuous Galerkin solution strategies for the under-resolved simulation of incompressible turbulent flows](https://mlsanity.com/paper/1809.00866/) (2018)

## Built on by (most cited first, 2 of 2)

- [Reinforcement learning for anisotropic p-adaptation and error estimation in high-order solvers](https://mlsanity.com/paper/2407.19000/) (2024)
- [Autonomous Adaptive Solver Selection for Chemistry Integration via Reinforcement Learning](https://mlsanity.com/paper/2604.00264/) (2026)

## Abstract (arXiv)

We explore a reinforcement learning strategy to automate and accelerate h/p-multigrid methods in high-order solvers. Multigrid methods are very efficient but require fine-tuning of numerical parameters, such as the number of smoothing sweeps per level and the correction fraction (i.e., proportion of the corrected solution that is transferred from a coarser grid to a finer grid). The objective of this paper is to use a proximal policy optimization algorithm to automatically tune the multigrid parameters and, by doing so, improve stability and efficiency of the h/p-multigrid strategy. Our findings reveal that the proposed reinforcement learning h/p-multigrid approach significantly accelerates and improves the robustness of steady-state simulations for one dimensional advection-diffusion and nonlinear Burgers' equations, when discretized using high-order h/p methods, on uniform and nonuniform grids.