A Personalised Learning Tool for Physics Undergraduate Students Built On a Large Language Model for Symbolic Regression

TL;DR

The paper addresses the challenge of personalized learning in undergraduate physics under interleaved practice by introducing an LLM-based tool that integrates symbolic regression and dimensional analysis. It systematically compares single-stage and two-stage prompting strategies, including the incorporation of Rayleigh's method, across 26 Feynman-lecture equations and 20 data points per equation. The results show that two-stage Rayleigh prompting offers the best balance of accuracy and efficiency, outperforming single-stage variants and approaching, yet not surpassing, specialized AI Feynman systems in speed. The work demonstrates that combining established physical reasoning (dimensional analysis, Rayleigh's method) with structured prompt engineering can yield a practical, data-driven supplement to traditional physics instruction, enabling personalized, scalable learning for undergraduates.

Abstract

Interleaved practice enhances the memory and problem-solving ability of students in undergraduate courses. We introduce a personalized learning tool built on a Large Language Model (LLM) that can provide immediate and personalized attention to students as they complete homework containing problems interleaved from undergraduate physics courses. Our tool leverages the dimensional analysis method, enhancing students' qualitative thinking and problem-solving skills for complex phenomena. Our approach combines LLMs for symbolic regression with dimensional analysis via prompt engineering and offers students a unique perspective to comprehend relationships between physics variables. This fosters a broader and more versatile understanding of physics and mathematical principles and complements a conventional undergraduate physics education that relies on interpreting and applying established equations within specific contexts. We test our personalized learning tool on the equations from Feynman's lectures on physics. Our tool can correctly identify relationships between physics variables for most equations, underscoring its value as a complementary personalized learning tool for undergraduate physics students.