Investigating LLM's Problem Solving Capability -- a Study on Statics Questions
Authors: Tanner Culleton, Hung-Fu Chang
Organizations: 1R. B, Annis School of Engineering, University of Indianapolis, Indianapolis, IN, 46227, USA
Abstract
Large Language Models (LLMs) have rapidly influenced many aspects of society, particularly education, due to their demonstrated ability to complete assignments and examinations across a wide range of subjects. Although prior studies have examined the educational impact of LLMs, much of the existing work relies on public or open problem datasets and lacks topic-specific analysis. In engineering education, especially within mechanical engineering, systematic investigations of LLM performance on specific problem types remain limited. Instead of using traditional methods that directly ask textbook questions to an LLM tool, our study adopts a model distillation process to evaluate LLM capabilities in solving statics problems. By distilling ChatGPT, we extracted 25 text-only statics questions and further constructed two additional datasets by adding diagrams and modifying their numerical values. Experimental results show that while LLMs perform well on text-only statics problems, their accuracy decreases when diagrams are introduced and the problems require multi-step reasoning. Further analysis suggests that this performance drop is not primarily caused by limitations in image recognition, but rather by difficulties in multi-step reasoning and in consistently applying extracted visual information across successive solution stages.
LLMs have shown strong performance in data-rich domains such as programming, but their reliability in engineering tasks remains limited. Circuit analysis is particularly challenging because it requires both multimodal understanding and precise mathematical reasoning. This paper presents an enhanced end-to-end circuit problem-solving framework using Gemini 2.5 Pro as the backbone model for scalable engineering-education applications. We systematically evaluate Gemini 2.5 Pro on undergraduate circuit-analysis problems and identify two major failure modes: circuit-recognition hallucinations, especially source-polarity errors, and reasoning-process hallucinations, such as incorrect current-direction assumptions. To reduce recognition errors, we integrate a fine-tuned YOLO detector with OpenCV-based processing to isolate voltage and current sources for polarity re-identification. To mitigate reasoning errors, we introduce an ngspice-driven verification loop that supports iterative refinement with optional human feedback. On 83 problems, the proposed pipeline achieves 97.59% accuracy, compared with 79.52% for baseline Gemini. Across four hand-drawn diagram variations, accuracy improves from 60.61%--71.21% to 89.39%--92.42%, with statistically significant gains (p<0.005). On 43 problems from a different textbook, accuracy increases from 58.14% to 83.72%, further supporting cross-textbook generalizability. Error analysis shows that circuit recognition remains the dominant source of residual failures, particularly under varying diagram representations. Overall, the framework substantially improves the robustness, scalability, and generalizability of LLM-based circuit problem solving for engineering education and practical circuit analysis.
Vision-Language Models (VLMs) demonstrate strong performance on general multimodal reasoning benchmarks, yet their ability to perform engineering reasoning remains largely unexplored. Unlike general visual question answering, engineering problem solving requires interpreting technical diagrams, selecting governing physical principles, and maintaining physically consistent multi-step reasoning. These capabilities are increasingly important for AI systems used in engineering education, scientific assistance, and technical decision-making, where reasoning failures may produce physically invalid yet superficially plausible solutions. Existing benchmarks primarily evaluate final answers and provide limited assessment of intermediate reasoning processes. We introduce EngVQA, a multimodal benchmark for evaluating engineering reasoning across 5 engineering subjects containing 696 problems. We introduce an 8-stage automatic evaluation framework for assessing VLM-generated solutions. The framework independently evaluates each stage of the solution, enabling fine-grained analysis of reasoning failures. We benchmark multiple state-of-the-art open and closed source VLMs on our evaluation framework and demonstrate substantial limitations in current engineering reasoning capabilities. Human evaluation shows strong agreement with our automated framework, achieving a Pearson correlation of 0.975 and a mean absolute error of 0.67 on a 10-point grading scale. Our results highlight the importance of process-oriented evaluation for reliable assessment of multimodal engineering reasoning systems.
Reasoning or inference-scaling models are the new generation of Large Language Models (LLMs) capable of complex problem solving. To investigate their problem-solving capability in physics, we evaluated model o4-mini by OpenAI on solving traditional, end-of-chapter problems from Halliday and Resnick's "Fundamentals of Physics," spanning core topics in the undergraduate physics curriculum. Performance was analyzed across modality and problem difficulty. The model solved the problems with overall accuracy of about 90%, but performance depended strongly on representation: accuracy was much higher on text-only problems (96%) than on problems requiring coordinated interpretation of text and images (79%). Accuracy also declined significantly as the problem difficulty increased from low to medium to high. These results show that state-of-the-art LLMs can solve much of the standard introductory physics problems, but that their performance remains uneven and constrained by problem modality and problem difficulty.