← 研踪 PaperTrailarXiv:2611.10433 · v1
HexIt: Learning Hexahedral Block Decomposition with Expert Iteration on Combinatorial Maps
首次提交 2026-11-07 11:25
版本更新 2026-11-07 11:25
雷达观测 2026-11-10 10:11
摘要
Decomposing a polyhedral solid into a few well-shaped hexahedral blocks is a long-standing open problem in mesh generation. We cast it as a sequential decision problem on a 3-dimensional generalised map: an agent splits edges, faces and volumes with three insert operations until every cell is a hexahedron and the mesh passes a quality threshold, and a policy that convolves over the map's involutions chooses each insert. A successful decomposition takes over a hundred decisions, and a uniformly random policy never finds one. We clone a policy from constructed decompositions and improve it by expert iteration. On held-out chamfered solids that share no boundary topology with the cloning data, the final policy solves an expected $94.4\%$ in $20$ samples, and expert iteration raises the best-of-20 solve rate on large chamfered solids from $0.203$ to $0.355$. At matched compute, PPO, GRPO and VinePPO updates all make the cloned policy worse.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-07 11:25 · 最新观测版本
HexIt: Learning Hexahedral Block Decomposition with Expert Iteration on Combinatorial Maps
Decomposing a polyhedral solid into a few well-shaped hexahedral blocks is a long-standing open problem in mesh generation. We cast it as a sequential decision problem on a 3-dimensional generalised map: an agent splits edges, faces and volumes with three insert operations until every cell is a hexahedron and the mesh passes a quality threshold, and a policy that convolves over the map's involutions chooses each insert. A successful decomposition takes over a hundred decisions, and a uniformly random policy never finds one. We clone a policy from constructed decompositions and improve it by expert iteration. On held-out chamfered solids that share no boundary topology with the cloning data, the final policy solves an expected $94.4\%$ in $20$ samples, and expert iteration raises the best-of-20 solve rate on large chamfered solids from $0.203$ to $0.355$. At matched compute, PPO, GRPO and VinePPO updates all make the cloned policy worse.
查看此版本解读 →查看此版本原文 ↗