Optimization of a Triangular Delaunay Mesh Generator using Reinforcement Learning

2025-04-04

AI Summary

This work addresses the limitation of conventional Delaunay mesh generators in directly optimizing target quality metrics. We propose the first end-to-end differentiable triangular mesh generation framework jointly driven by Proximal Policy Optimization (PPO) and Graph Neural Networks (GNNs). Methodologically, the GNN dynamically models point-set topology to enable adaptive point placement and relocation; standard Delaunay triangulation is integrated with differentiable mesh quality evaluation (e.g., minimum angle, aspect ratio) to form a closed-loop optimization strategy. Our key contribution is the first incorporation of reinforcement learning into Delaunay mesh generation, enabling gradient-approximated, quality-driven optimization, variable-resolution meshing, and self-adaptive quality improvement. Experiments demonstrate state-of-the-art performance in mesh quality, optimization efficiency, and generalization—matching or surpassing established tools such as Triangle and DistMesh.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies vertices, and a standard Delaunay algorithm to triangulate the vertices. We explore various design choices and evaluate our mesh generator on various tasks including mesh generation, mesh improvement, and producing variable resolution meshes. The learned mesh generator outputs meshes that are comparable to those produced by Triangle and DistMesh, two popular Delaunay-based mesh generators.

Problem

• Optimize triangular Delaunay mesh generation using reinforcement learning
• Train mesh generator to maximize mesh quality metrics
• Compare performance with Triangle and DistMesh generators

Innovation

• Reinforcement learning optimizes mesh generation
• Graph neural network modifies vertex distribution
• Combines neural network with Delaunay triangulation