arXiv subjects

Stefan Petersen

Publications and source records attributed to Stefan Petersen.

4 recordsLinked to original sources

arXiv2026

Developing an LLM-Based Feedback System Grounded in Evidence-Centered Design to Support Physics Problem Solving

Generative AI offers new opportunities for individualized and adaptive learning, e.g., through large language model (LLM)-based feedback systems. While LLMs can produce factually correct feedback for relatively straightforward conceptual tasks, delivering high-quality feedback for tasks that require advanced domain expertise, such as physics problem solving, remains a substantial challenge. This study presents the design and implementation of an LLM-based feedback system for physics problem solving grounded in evidence-centered design and reports a first evaluation within the German Physics Olympiad. Participants rated the usefulness and correctness of the generated feedback for each implemented problem. The collected ratings indicate that the feedback was generally perceived as useful and highly correct. However, an in-depth analysis revealed that the feedback contained errors in 20% of cases; errors that often went unnoticed by the students. We discuss the risks associated with uncritical reliance on LLM-based feedback and outline potential directions for generating more adaptive and reliable LLM-based feedback in the future.

physics.ed-ph↗

arXiv2025

Evaluating GPT- and Reasoning-based Large Language Models on Physics Olympiad Problems: Surpassing Human Performance and Implications for Educational Assessment

Large language models (LLMs) are now widely accessible, reaching learners at all educational levels. This development has raised concerns that their use may circumvent essential learning processes and compromise the integrity of established assessment formats. In physics education, where problem solving plays a central role in instruction and assessment, it is therefore essential to understand the physics-specific problem-solving capabilities of LLMs. Such understanding is key to informing responsible and pedagogically sound approaches to integrating LLMs into instruction and assessment. This study therefore compares the problem-solving performance of a general-purpose LLM (GPT-4o, using varying prompting techniques) and a reasoning-optimized model (o1-preview) with that of participants of the German Physics Olympiad, based on a set of well-defined Olympiad problems. In addition to evaluating the correctness of the generated solutions, the study analyzes characteristic strengths and limitations of LLM-generated solutions. The findings of this study indicate that both tested LLMs (GPT-4o and o1-preview) demonstrate advanced problem-solving capabilities on Olympiad-type physics problems, on average outperforming the human participants. Prompting techniques had little effect on GPT-4o's performance, while o1-preview almost consistently outperformed both GPT-4o and the human benchmark. Based on these findings, the study discusses implications for the design of summative and formative assessment in physics education, including how to uphold assessment integrity and support students in critically engaging with LLMs.

physics.ed-ph↗

arXiv2006

Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons

In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space C^k/S_k features a natural K"ahler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.

hep-th↗

arXiv2005

Sigma-Model Solitons in the Noncommutative Plane: Construction and Stability Analysis

Noncommutative multi-solitons are investigated in Euclidean two-dimensional U(n) and Grassmannian sigma models, using the auxiliary Fock-space formalism. Their construction and moduli spaces are reviewed in some detail, unifying abelian and nonabelian configurations. The analysis of linear perturbations around these backgrounds reveals an unstable mode for the U(n) models but shows stability for the Grassmannian case. For multi-solitons which are diagonal in the Fock-space basis we explicitly evaluate the spectrum of the Hessian and identify all zero modes. It is very suggestive but remains to be proven that our results qualitatively extend to the entire multi-soliton moduli space.

hep-th↗