# Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation

arXiv: https://arxiv.org/abs/2606.10601 · HTML: https://mlsanity.com/paper/2606.10601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Hybrid Actor-Critic Reinforcement Learning in Parameterized Action Space](https://mlsanity.com/paper/1903.01344/) (2019)
- [Discrete and Continuous Action Representation for Practical RL in Video Games](https://mlsanity.com/paper/1912.11077/) (2019)
- [MeshingNet: A New Mesh Generation Method based on Deep Learning](https://mlsanity.com/paper/2004.07016/) (2020)
- [Reinforcement learning for automatic quadrilateral mesh generation: a soft actor-critic approach](https://mlsanity.com/paper/2203.11203/) (2022)
- [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)
- [Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modeling](https://mlsanity.com/paper/2504.11383/) (2025)
- [Discretionary Lane-Change Decision and Control via Parameterized Soft Actor-Critic for Hybrid Action Space](https://mlsanity.com/paper/2402.15790/) (2024)
- [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)

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

- [Playing to Par: Reinforcement Learning for Provably Optimal Quadrilateral Block Decompositions](https://mlsanity.com/paper/2609.32146/) (2026)

## Abstract (arXiv)

Generating high-quality meshes for arbitrary geometries remains a fundamental bottleneck in computational engineering, often demanding heuristic tuning and semi-manual workflows. In this paper, we introduce Dmsh, a first fully automated reinforcement learning pipeline that unifies geometric decomposition and quadrilateral mesh generation within a single learning-based framework. Dmsh decomposes the problem through three coordinated agents handling topology simplification, geometric regularization, and mesh generation. The meshing process is formulated as a Markov Decision Process and solved using a parametric Soft Actor-Critic architecture with decoupled critics, enabling efficient exploration of a hybrid discrete-continuous action space. A curriculum learning strategy ensures scalability from simple domains to highly complex geometries, suppressing seed variance. By design, the recursive decomposition enables parallel meshing of subregions, yielding globally conforming all-quadrilateral meshes without post hoc correction. Across a wide range of benchmarks, Dmsh consistently outperforms existing methods in automation, robustness, and mesh quality, establishing a new paradigm for learning-based mesh generation.