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Dmsh introduces a novel multi-agent reinforcement learning framework that fully automates all-quadrilateral mesh generation, effectively eliminating the need for heuristic tuning and semi-manual workflows common in computational engineering. By formulating the meshing process as a Markov Decision Process solved with a parametric Soft Actor-Critic architecture, the system achieves superior automation, robustness, and mesh quality across complex geometries. This approach establishes a new paradigm for learning-based mesh generation, offering significant potential to streamline fundamental bottlenecks in numerical analysis and simulation.
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Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation

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arXiv:2606.10601v1 Announce Type: cross 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.

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.

Numerical Analysis (math.NA); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2606.10601 [math.NA]

(or arXiv:2606.10601v1 [math.NA] for this version)

https://doi.org/10.48550/arXiv.2606.10601 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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