GReFEM: Multimodal LLMs as Zero-Shot Semantic Assistants for Physics-Guided 3D Mesh Refinement

Adaptive volumetric finite element meshing traditionally requires iterative PDE solvers or heavily supervised, data-driven surrogates trained on large-scale simulation data. This work explores a significant question: can the high-level semantic understanding of off-the-shelf MLLMs serve as a viable, zero-shot geometric proxy for finite element mesh refinement? We introduce GReFEM (Geometric Reasoning Enhanced Multimodal LLMs for Finite Element Meshing), a framework that utilizes MLLMs to visually localize stress-critical regions based on physics-guided textual prompts. To bridge the gap between 2D MLLM pre-training and 3D geometries, we introduce orthoViews, a trained view-selection module that assists these MLLMs by maximizing the observability of key geometric features. We evaluate GReFEM by computing finite-element error at stress concentrations, on diverse CAD mesh geometries under multiple loading cases, with MLLMs and prompt variants, against blind and load-informed geometric heuristics, solver-informed Zienkiewicz--Zhu (ZZ) refinement, and a retrained learned adaptive-meshing baseline, all at a matched element budget. Without any FEM solve or simulation training data, GReFEM lowers the critical-region peak von Mises stress error relative to a blind geometric heuristic and to refinement driven by a coarse FEM solve, closing 58% of the gap between the unrefined mesh and a reference-solve oracle, while a hand-derived analytical load-informed heuristic remains stronger and the learned baseline performs slightly better overall. With this we investigate their performance as semantic assistants in automated simulation workflows. Code is available at https://github.com/kbali1297/GReFEM