Playing to Par: Reinforcement Learning for Provably Optimal Quadrilateral Block Decompositions
An RL agent produces provably optimal quadrilateral meshes that outperform Gmsh on held-out domains.
The paper trains a reinforcement-learning agent to build all-quadrilateral block decompositions that reach the discrete Gauss-Bonnet lower bound on total vertex irregularity, called par. The policy edits a half-edge mesh using convolutions that follow mesh connectivity, is initialized by behaviour cloning on optimal meshes walked backward into demonstrations, and is then trained with PPO. On 96 held-out domains it produces a complete mesh on every domain, a usable one on 95.7 on average, and a provably optimal one on 90, while Gmsh at the same element count completes 51, is usable on 38, and is optimal on none. On 64 domains twice the training size it completes all, is usable on 62, and keeps median excess over par below one.
- The agent targets the Gauss-Bonnet lower bound on vertex irregularity, called par.
- Behaviour cloning from reversed optimal meshes, then PPO, overcomes sparse rewards.
- On 96 held-out domains it finishes all and is provably optimal on 90; Gmsh on none.
- On 64 double-size domains, median excess over par stays below one.
- Tags
- reinforcement-learningmesh-generationquadrilateralppobehaviour-cloningcomputational-geometrygmsh
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From the original article
1 min read at huggingface.co
A quadrilateral block decomposition of a planar domain is judged by whether it is complete, whether its elements are well shaped, and how many of its vertices are irregular. The last has a provable floor: the discrete Gauss-Bonnet identity enforces a lower bound on the total vertex irregularity of any all-quadrilateral mesh of a given domain purely based on its topology and corner angles.
By Arjun Narayanan, Per-Olof Persson · huggingface.co
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