用大模型当数学建模助手，能自动分析问题并生成完整解法。
MM-Agent: LLM as Agents for Real-world Mathematical Modeling Problem
- 分四步构建模型：分析问题、形式化建模、求解计算、生成报告
- 在111个真实题目上表现超人类专家11.88%，每题仅需15分钟和0.88美元
- 已助大学生团队获建模竞赛前2%，适合科研与工程建模场景
数学建模是科学发现与工程实践的核心，将现实问题转化为物理、生物、经济等领域的形式系统。不同于预设公式的数学推理，建模需开放式分析、抽象与严谨形式化。尽管大语言模型具备强大推理能力，但在严格建模构造方面仍有不足。为此，我们定义了基于大模型的现实数学建模任务，要求代理完成问题分析、领域适配建模与端到端求解。提出MM-Bench基准，包含2000至2025年数学建模竞赛（MCM/ICM）中的111道题目，覆盖十大学科领域。设计MM-Agent框架，将建模过程分解为四个阶段：开放问题分析、结构化建模、计算求解与报告生成。在MM-Bench上的实验表明，MM-Agent显著优于基线代理，在使用GPT-4o时比人类专家提升11.88%，每任务耗时15分钟，成本仅0.88美元。在正式竞赛协议下，其辅助两支本科生团队获得2025年MCM/ICM Finalist Award（前2.0%，共27,456支队伍），验证了作为建模协作者的实际效能。代码已开源。
原文摘要 · Abstract (English)
Mathematical modeling is a cornerstone of scientific discovery and engineering practice, enabling the translation of real-world problems into formal systems across domains such as physics, biology, and economics. Unlike mathematical reasoning, which assumes a predefined formulation, modeling requires open-ended problem analysis, abstraction, and principled formalization. While Large Language Models (LLMs) have shown strong reasoning capabilities, they fall short in rigorous model construction, limiting their utility in real-world problem-solving. To this end, we formalize the task of LLM-powered real-world mathematical modeling, where agents must analyze problems, construct domain-appropriate formulations, and generate complete end-to-end solutions. We introduce MM-Bench, a curated benchmark of 111 problems from the Mathematical Contest in Modeling (MCM/ICM), spanning the years 2000 to 2025 and across ten diverse domains such as physics, biology, and economics. To tackle this task, we propose MM-Agent, an expert-inspired framework that decomposes mathematical modeling into four stages: open-ended problem analysis, structured model formulation, computational problem solving, and report generation. Experiments on MM-Bench show that MM-Agent significantly outperforms baseline agents, achieving an 11.88\% improvement over human expert solutions while requiring only 15 minutes and \$0.88 per task using GPT-4o. Furthermore, under official MCM/ICM protocols, MM-Agent assisted two undergraduate teams in winning the Finalist Award (\textbf{top 2.0\% among 27,456 teams}) in MCM/ICM 2025, demonstrating its practical effectiveness as a modeling copilot. Our code is available at https://github.com/usail-hkust/LLM-MM-Agent
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