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

Adaptive volumetric finite element meshing is a critical step in computer-aided engineering and analysis that dictates the computational budget of a given problem. It traditionally requires iterative PDE solvers or heavily supervised, data-driven surrogates trained on large-scale simulation data. While Multimodal Large Language Models (MLLMs) excel in 2D visual tasks, their zero-shot capability to semantically ground regions based on geometric understanding and physics remains an open question. Overall, this study 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? To investigate this, 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 view-selection module that maximizes the observability of key geometric features. We conduct an in-depth empirical evaluation across diverse CAD geometries, loading cases, and SOTA MLLMs, comparing them against a tuned geometric heuristic under a strict, matched refinement budget. Our findings reveal that MLLMs demonstrate robust zero-shot capacity to accurately follow complex spatial-physical instructions, isolating stress-relevant features with higher precision than blind heuristics. By mapping both the successes and current limitations of MLLMs in physical grounding, this study defines the frontier of foundation models as semantic assistants in automated simulation workflows.