FEVessel: Mesh-Independent Analysis of 3D Pressure Vessels with the Label-Free Pretrained Finite Element Method
Pressure vessel analysis in the chemical, nuclear, and new-energy industries requires solving the same elasticity problem across many materials, geometries, and loads, where mesh quality and repeated solving govern both accuracy and cost. The finite element method (FEM) cannot amortise this repeated cost and fails on degenerate meshes, while the neural operators meant to replace it still need labelled data that FEM must generate. This paper proposes FEVessel, an adaptation of the Pretrained Finite Element Method (PFEM) to three-dimensional (3D) pressure vessels, and validates four capabilities across the two limitations above. FEVessel i) encodes each vessel as a point cloud with coordinate, material, and load channels, ii) pretrains a Transolver operator on the total potential energy instead of FEM labels, and iii) warm-starts iterative solvers with its prediction. A single model generalises across material, geometry, and boundary conditions at a $1.35\%$ relative displacement error, and its $2.07\%$ strain error is about $4.7$ times lower than that of a supervised Fourier neural operator ($9.72\%$), whose structured grid cannot preserve the through-thickness strain. Its warm start cuts algebraic multigrid iterations from $195$ to $18$, a $9.2\times$ end-to-end wall-clock speedup at the $10^{-3}$ engineering tolerance. The model transfers across mesh resolutions without retraining, holding about $3\%$ error at only $30\%$ of the training point density. On inverted and sliver meshes where FEM fails, the error remains below $3.66\%$. To our knowledge, this is the first systematic study of mesh-independent solution on industrially relevant 3D pressure vessels with degenerate meshes. Because training needs no labels, FEVessel works exactly where FEM cannot supply any, removing manual mesh repair from the analysis pipeline.