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

2026-06-09

AI Summary

This work addresses the long-standing challenge of automatically generating high-quality all-quadrilateral meshes for arbitrary geometries by introducing the first unified multi-agent reinforcement learning framework that jointly optimizes geometric decomposition and mesh generation. The meshing process is formulated as a Markov decision process, wherein three cooperative agents—responsible for topological simplification, geometric regularization, and quadrilateral mesh generation—operate in an end-to-end pipeline. Leveraging a parameterized decoupled Soft Actor-Critic algorithm, a hybrid discrete-continuous action space, and a curriculum learning strategy, the method enables recursive and parallel processing of subregions without requiring post-processing. It produces globally consistent all-quad meshes and significantly outperforms existing approaches across diverse complex geometric benchmarks, achieving notable advances in automation, robustness, and mesh quality.

Abstract

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.

Problem

• all-quad mesh generation
• computational engineering
• mesh quality
• geometric decomposition
• automation

Innovation

• multi-agent reinforcement learning
• all-quad mesh generation
• geometric decomposition
• Soft Actor-Critic
• curriculum learning