AI University: An LLM-Powered Learning Assistant for Engineering---A Finite Element Method Case Study

We introduce AI University (AI-U), a flexible framework for AI-driven course content delivery that adapts to a course's instructional style. AI-U combines a fine-tuned large language model (LLM) with retrieval-augmented generation (RAG) and a reasoning synthesis model to generate style-aligned responses from lecture videos, notes, and textbooks. Using a graduate-level finite-element-method (FEM) course as a case study, we present a pipeline to synthesize course-grounded training data, fine-tune an open-source LLM with Low-Rank Adaptation (LoRA), and apply RAG-based synthesis. Our evaluation---combining cosine similarity, LLM-based assessment, expert review, and user studies---shows improved alignment with course materials relative to the base model. We have also developed a prototype web application, available at https://my-ai-university.com, that enhances AI-generated responses with references to relevant sections of the course material and clickable links to time-stamped video lectures. Our expert model is found to be higher scoring by a quantitative measure on 86% of test cases. An LLM judge also preferred our expert model to its base model under both evaluation prompts. Human evaluation by advanced users showed a preference for our expert model approximately twice as often as for the base model. The FEM course instructor found our expert model to achieve better alignment with class-specific content than a recent closed-weight model when both were combined with the reasoning synthesis model. AI-U offers a practical approach to developing course-specific learning assistants using fine-tuned and retrieval-augmented LLMs. By presenting our framework in an FEM class---central to training PhD and master's students in engineering science---we offer a template with potential for extension across STEM fields.