# GNNRL-Smoothing: A Prior-Free Reinforcement Learning Model for Mesh Smoothing

arXiv: https://arxiv.org/abs/2410.19834 · HTML: https://mlsanity.com/paper/2410.19834/

## 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 13 of its 58 references that are in the map.
- First posted on arXiv 19 Oct 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, 13 of 13)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [A Closer Look at Invalid Action Masking in Policy Gradient Algorithms](https://mlsanity.com/paper/2006.14171/) (2020)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)
- [E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation](https://mlsanity.com/paper/2207.11233/) (2022)
- [Proposing an intelligent mesh smoothing method with graph neural networks](https://mlsanity.com/paper/2311.12815/) (2023)

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

- [UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Loss](https://mlsanity.com/paper/2508.08615/) (2025)

## Abstract (arXiv)

Mesh smoothing methods can enhance mesh quality by eliminating distorted elements, leading to improved convergence in simulations. To balance the efficiency and robustness of traditional mesh smoothing process, previous approaches have employed supervised learning and reinforcement learning to train intelligent smoothing models. However, these methods heavily rely on labeled dataset or prior knowledge to guide the models' learning. Furthermore, their limited capacity to enhance mesh connectivity often restricts the effectiveness of smoothing. In this paper, we first systematically analyze the learning mechanisms of recent intelligent smoothing methods and propose a prior-free reinforcement learning model for intelligent mesh smoothing. Our proposed model integrates graph neural networks with reinforcement learning to implement an intelligent node smoothing agent and introduces, for the first time, a mesh connectivity improvement agent. We formalize mesh optimization as a Markov Decision Process and successfully train both agents using Twin Delayed Deep Deterministic Policy Gradient and Double Dueling Deep Q-Network in the absence of any prior data or knowledge. We verified the proposed model on both 2D and 3D meshes. Experimental results demonstrate that our model achieves feature-preserving smoothing on complex 3D surface meshes. It also achieves state-of-the-art results among intelligent smoothing methods on 2D meshes and is 7.16 times faster than traditional optimization-based smoothing methods. Moreover, the connectivity improvement agent can effectively enhance the quality distribution of the mesh.