Transcendental equations requiring iterative numerical solution pervade engineering practice, from fluid mechanics friction factor calculations to orbital position determination. We systematically evaluate whether Large Language Models can solve these equations through direct numerical prediction or whether a hybrid architecture combining LLM symbolic manipulation with classical iterative solvers proves more effective. Testing six state-of-the-art models (GPT-5.1, GPT-5.2, Gemini-3-Flash, Gemini-2.5-Lite, Claude-Sonnet-4.5, Claude-Opus-4.5) on 100 problems spanning seven engineering domains, we compare direct prediction against solver-assisted computation where LLMs formulate governing equations and provide initial conditions while Newton-Raphson iteration performs numerical solution. Direct prediction yields mean relative errors of 0.765 to 1.262 across models, while solver-assisted computation achieves 0.225 to 0.301, representing error reductions of 67.9% to 81.8%. Domain-specific analysis reveals dramatic improvements in Electronics (93.1%) due to exponential equation sensitivity, contrasted with modest gains in Fluid Mechanics (7.2%) where LLMs exhibit effective pattern recognition. These findings establish that contemporary LLMs excel at symbolic manipulation and domain knowledge retrieval but struggle with precision-critical iterative arithmetic, suggesting their optimal deployment as intelligent interfaces to classical numerical solvers rather than standalone computational engines.
From Natural Language to Solver-Ready Power System Optimization: An LLM-Assisted, Validation-in-the-Loop Framework
Department of Electrical and Computer Engineering（电气与计算机工程系）；University of Southern California（南加州大学）；Department of Electrical Engineering（电气工程系）；University of Texas at Arlington（德克萨斯大学阿灵顿分校）；Interdisciplinary Science Department（跨学科科学系）；Brookhaven National Laboratory（布鲁赫斯国家实验室）
PT-PINNs: A Parametric Engineering Turbulence Solver based on Physics-Informed Neural Networks
Zhejiang University（浙江大学）；Shanghai Institute for Advanced Study of Zhejiang University（浙江大学上海高等研究院）；State Key Laboratory of Clean Energy Utilization（清洁能源利用国家重点实验室）
A Quantum-Assisted Agentic Distributed Artificial Intelligence Framework for Deadline-Bounded Orchestration of Hybrid Renewable Microgrids
Philips University（菲利普斯大学）；University of Cyprus（塞浦路斯大学）；CYENS Centre of Excellence（CYENS卓越中心）；Japan Advanced Institute of Science and Technology（日本先端科学技术大学院大学）；Doshisha University（同志社大学）
Governing AI-Assisted Security Operations: A Design Science Framework for Operational Decision Support
Department of Artificial Intelligence, University of the Cumberlands（人工智能系，坎伯兰大学）；Department of Management Information Systems, University of Illinois Springfield（管理信息系统系，伊利诺伊大学斯普林菲尔德分校）
The Role of Instructional Guidance in Generative AI-Assisted Learning: Empirical Evidence from Construction Engineering Education
Dept. of Civil, Environmental, and Geospatial Engineering, Michigan Technological Univ.（土木、环境与地理空间工程系，密歇根技术大学）；Dept. of Civil and Construction Engineering, Western Michigan Univ.（土木与建设工程系，西部密歇根大学）；Dept. of Psychology and Human Factors, Michigan Technological Univ.（心理学与人因工程系，密歇根技术大学）
KAYROS: An Anytime and Exact Open-Source Solver for Duration-Minimization Time-Dependent Vehicle Routing. A Technical Report and a Case Study in Human-AI Engineering
