# A reinforcement learning strategy for p-adaptation in high order solvers

arXiv: https://arxiv.org/abs/2306.08292 · HTML: https://mlsanity.com/paper/2306.08292/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [A review on Deep Reinforcement Learning for Fluid Mechanics](https://mlsanity.com/paper/1908.04127/) (2019)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)
- [Deep Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2209.12351/) (2022)
- [Learning Controllable Adaptive Simulation for Multi-resolution Physics](https://mlsanity.com/paper/2305.01122/) (2023)
- [Improving aircraft performance using machine learning: a review](https://mlsanity.com/paper/2210.11481/) (2022)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2211.00801/) (2022)

## Built on by (most cited first, 4 of 4)

- [Transfer learning-enhanced deep reinforcement learning for aerodynamic airfoil optimisation subject to structural constraints](https://mlsanity.com/paper/2505.02634/) (2025)
- [Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards](https://mlsanity.com/paper/2406.08440/) (2024)
- [A reinforcement learning strategy to automate and accelerate h/p-multigrid solvers](https://mlsanity.com/paper/2407.15872/) (2024)
- [Reinforcement learning for anisotropic p-adaptation and error estimation in high-order solvers](https://mlsanity.com/paper/2407.19000/) (2024)

## Abstract (arXiv)

Reinforcement learning (RL) has emerged as a promising approach to automating decision processes. This paper explores the application of RL techniques to optimise the polynomial order in the computational mesh when using high-order solvers. Mesh adaptation plays a crucial role in improving the efficiency of numerical simulations by improving accuracy while reducing the cost. Here, actor-critic RL models based on Proximal Policy Optimization offer a data-driven approach for agents to learn optimal mesh modifications based on evolving conditions. The paper provides a strategy for p-adaptation in high-order solvers and includes insights into the main aspects of RL-based mesh adaptation, including the formulation of appropriate reward structures and the interaction between the RL agent and the simulation environment. We discuss the impact of RL-based mesh p-adaptation on computational efficiency and accuracy. We test the RL p-adaptation strategy on a 1D inviscid Burgers' equation to demonstrate the effectiveness of the strategy. The RL strategy reduces the computational cost and improves accuracy over uniform adaptation, while minimising human intervention.