# Reinforcement learning for automatic quadrilateral mesh generation: a soft actor-critic approach

arXiv: https://arxiv.org/abs/2203.11203 · HTML: https://mlsanity.com/paper/2203.11203/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 79 references that are in the map.
- First posted on arXiv 19 Mar 2022.

## Builds on (most cited first, 26 of 26)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Benchmarking Deep Reinforcement Learning for Continuous Control](https://mlsanity.com/paper/1604.06778/) (2016)
- [Challenges of Real-World Reinforcement Learning](https://mlsanity.com/paper/1904.12901/) (2019)
- [StarCraft II: A New Challenge for Reinforcement Learning](https://mlsanity.com/paper/1708.04782/) (2017)
- [Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents](https://mlsanity.com/paper/1709.06009/) (2017)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [Behaviour Suite for Reinforcement Learning](https://mlsanity.com/paper/1908.03568/) (2019)
- [State Representation Learning for Control: An Overview](https://mlsanity.com/paper/1802.04181/) (2018)
- [Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformation](https://mlsanity.com/paper/1908.01491/) (2019)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)
- [MeshingNet: A New Mesh Generation Method based on Deep Learning](https://mlsanity.com/paper/2004.07016/) (2020)

## Built on by (most cited first, 17 of 17)

- [Deep Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2209.12351/) (2022)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [SRL-Assisted AFM: Generating Planar Unstructured Quadrilateral Meshes with Supervised and Reinforcement Learning-Assisted Advancing Front Method](https://mlsanity.com/paper/2305.00540/) (2023)
- [Quasi-optimal hp-finite element refinements towards singularities via deep neural network prediction](https://mlsanity.com/paper/2209.05844/) (2022)
- [Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2211.00801/) (2022)
- [Point2Quad: Generating Quad Meshes from Point Clouds via Face Prediction](https://mlsanity.com/paper/2504.19545/) (2025)
- [A Survey of AI Methods for Geometry Preparation and Mesh Generation in Engineering Simulation](https://mlsanity.com/paper/2512.23719/) (2025)
- [Reinforcement Learning for Block Decomposition of CAD Models](https://mlsanity.com/paper/2302.11066/) (2023)
- [Learning topological operations on meshes with application to block decomposition of polygons](https://mlsanity.com/paper/2309.06484/) (2023)
- [Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards](https://mlsanity.com/paper/2406.08440/) (2024)
- [Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation](https://mlsanity.com/paper/2606.10601/) (2026)
- [Digital Engineering Transformation with Trustworthy AI towards Industry 4.0: Emerging Paradigm Shifts](https://mlsanity.com/paper/2301.00951/) (2023)
- [LLQL: Logistic Likelihood Q-Learning for Reinforcement Learning](https://mlsanity.com/paper/2307.02345/) (2023)
- [Playing to Par: Reinforcement Learning for Provably Optimal Quadrilateral Block Decompositions](https://mlsanity.com/paper/2609.32146/) (2026)
- [Q-MAGIC: Quad-only Mesh Autoregressive Generation via Singularity-Aware Circular Relative Offset Tokenization](https://mlsanity.com/paper/2610.19777/) (2026)

## Abstract (arXiv)

This paper proposes, implements, and evaluates a reinforcement learning (RL)-based computational framework for automatic mesh generation. Mesh generation plays a fundamental role in numerical simulations in the area of computer aided design and engineering (CAD/E). It is identified as one of the critical issues in the NASA CFD Vision 2030 Study. Existing mesh generation methods suffer from high computational complexity, low mesh quality in complex geometries, and speed limitations. These methods and tools, including commercial software packages, are typically semiautomatic and they need inputs or help from human experts. By formulating the mesh generation as a Markov decision process (MDP) problem, we are able to use a state-of-the-art reinforcement learning (RL) algorithm called "soft actor-critic" to automatically learn from trials the policy of actions for mesh generation. The implementation of this RL algorithm for mesh generation allows us to build a fully automatic mesh generation system without human intervention and any extra clean-up operations, which fills the gap in the existing mesh generation tools. In the experiments to compare with two representative commercial software packages, our system demonstrates promising performance with respect to scalability, generalizability, and effectiveness.