Arjun Narayanan

The work casts quadrilateral block decomposition as a Markov decision process over a half-edge mesh, uses the vertex-irregularity lower bound implied by the discrete Gauss–Bonnet identity (called par) as both reward target and termination test, and trains via behaviour cloning on trivially constructible optimal meshes followed by PPO, producing an all-quadrilateral mesh on all 96 held-out domains, a usable one on 95.7 on average and a provably optimal one on 90, whereas Gmsh's strongest configuration at the same element count completes 51, is usable on 38 and optimal on none.

The work casts quadrilateral block decomposition as a Markov decision process over a half-edge mesh, uses the vertex-irregularity lower bound implied by the discrete Gauss–Bonnet identity (called par) as both reward target and termination test, and trains via behaviour cloning on trivially constructible optimal meshes followed by PPO, producing an all-quadrilateral mesh on all 96 held-out domains, a usable one on 95.7 on average and a provably optimal one on 90, whereas Gmsh's strongest configuration at the same element count completes 51, is usable on 38 and optimal on none.