🤖 AI Summary
This work proposes a measurement-driven, constrained natural language interface architecture to reduce manual configuration overhead in finite element simulations while mitigating the risk of unreliable code generation by large language models (LLMs) in critical solver stages. The approach confines the LLM to front-end tasks—such as prompt parsing and Gmsh script generation for non-standard geometries—while a deterministic scheduler orchestrates verified FEniCS/UFL templates for core computations across five multiphysics problem classes: linear elasticity, hyperelasticity, elastoplasticity, thermomechanical coupling, and phase-field fracture. Experimental results demonstrate 100% prompt parsing success, 97.1% field extraction accuracy, and 90% success rate in custom geometry generation. Simulation accuracy reaches sub-percent levels for smooth problems, with errors in nonlinear cases maintained within 2–5%.
📝 Abstract
Large language models can reduce the manual effort required to set up finite element simulations, but they introduce reliability risks when generated solver code lies on the critical path. We present a constrained natural-language interface for multi-physics finite element analysis in which the LLM is limited to front-end tasks: parsing prompts into structured JSON, generating Gmsh code only for non-catalog geometries, and using retry feedback for those stages. It never writes FEniCS solver templates, derives weak forms, or writes the numerical solver core. A deterministic dispatcher maps the validated specification to five human-written FEniCS/UFL templates: linear elasticity, hyperelasticity, elastoplasticity, thermo-mechanical coupling, and phase-field fracture. We validate this deterministic template layer against analytical solutions and published 2D/3D benchmarks. Smooth cases reach sub-percent agreement on adequate meshes, while harder nonlinear cases reach the 2-5 percent range. We also evaluate the LLM-facing front end directly. In a 15-prompt parser benchmark, first-pass valid parses were obtained for 9 cases, and all remaining cases were repaired after retry, giving a final valid parse rate of 100.0 percent, 100.0 percent problem-class accuracy, and 97.1 percent field-extraction accuracy. In a 10-case custom-geometry benchmark routed through the real LLM-to-Gmsh path, first-pass and final success were both 90.0 percent, with one unrecovered invalid-geometry failure. These results show that the parser and constrained prompt/validation design are effective on these benchmarks. As an end-to-end demonstration, the system generates and analyzes a 3D elastoplastic L-bracket with a fillet and bolt hole from one natural-language prompt. The contribution is a measured architecture for natural-language-driven variational simulation, not open-ended autonomous code generation.