Large Language Models for Mathematical Modeling: A Literature Survey

The Hong Kong University of Science and Technology (Guangzhou)

Data Science and Analytics Thrust

PhD Qualifying Examination

By Mr. WU, Xiaojun

Abstract

Large language models (LLMs) are increasingly used to translate natural language descriptions of real-world problems into mathematical formulations, computational procedures, and written solution reports. This review synthesizes a focused source-bounded corpus of four core works: Mamo, ModelingAgent, MM-Agent, and a DeepSeek-R1 dissertation on supply-chain operations research. It situates these works against the broader practice of contest-style mathematical modeling, where teams must choose assumptions, select methods, compute results, and communicate them in a research-style report. It also integrates adjacent AI literature on four major modeling domains: differential equations, operations research optimization, data science, and multi-criteria decision making. The review is bounded by source materials and bibliographic entries traceable to project BibTeX, bibliography, PDF, or LaTeX files. It does not introduce unverified external references.

The literature shows a clear shift from answer-oriented mathematical reasoning benchmarks toward process-oriented evaluation of modeling. Mamo uses solvers to isolate formulation quality from downstream computation, while ModelingAgent and MM-Agent expand the task to open-ended competition-style modeling that requires problem analysis, assumption design, method retrieval, tool use, computation, and report generation. Adjacent method-domain works provide important capabilities, but they mostly focus on method formalization, algorithmic performance, or task automation; this review reframes them as components of a larger modeling workflow. Across these works, the central finding is that LLM-for-mathematical-modeling should be evaluated as an integrated workflow rather than as a single-step reasoning task. Future research should prioritize traceable formulation, method-aware harnesses, human-calibrated evaluation, uncertainty-aware tool use, and reproducible benchmark protocols.

Keywords: large language models; mathematical modeling; LLM agents; operations research; benchmark evaluation; solver verification

PQE Committee

Chair: Prof. CHU, Xiaowen

Prime Supervisor: Prof. LI, Jia

Co-Supervisor: Prof. GUO, Jian (Online)

Examiner: Prof. DING, Zishuo