[2603.21011] ALL-FEM: Agentic Large Language models Fine-tuned for Finite Element Methods

Computer Science > Computational Engineering, Finance, and Science arXiv:2603.21011 (cs) [Submitted on 8 Jan 2026] Title:ALL-FEM: Agentic Large Language models Fine-tuned for Finite Element Methods Authors:Rushikesh Deotale, Adithya Srinivasan, Yuan Tian, Tianyi Zhang, Pavlos Vlachos, Hector Gomez View a PDF of the paper titled ALL-FEM: Agentic Large Language models Fine-tuned for Finite Element Methods, by Rushikesh Deotale and 5 other authors View PDF HTML (experimental) Abstract:Finite element (FE) analysis guides the design and verification of nearly all manufactured objects. It is at the core of computational engineering, enabling simulation of complex physical systems, from fluids and solids to multiphysics systems. However, implementing FE codes and analyzing simulation results demands expertise across numerical analysis, continuum mechanics, and programming. Conventional Large Language Models (LLMs) can generate FE code, but they hallucinate, lack awareness of variational structures, and cannot close the loop from problem statement to a verified solution. Here, we propose ALL-FEM, an autonomous simulation system that integrates agentic AI with domain-specific, fine-tuned LLMs for FEniCS code generation across solid, fluid, and multiphysics applications. We construct a corpus of 1000+ verified FEniCS scripts by combining 500+ curated expert codes with a retrieval-augmented, multi-LLM pipeline that generates and filters codes for diverse PDEs, geometries, and boundar...