# ModelingAgent: Bridging LLMs and Mathematical Modeling for Real-World Challenges

arXiv: https://arxiv.org/abs/2505.15068 · HTML: https://mlsanity.com/paper/2505.15068/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 61 references that are in the map.
- First posted on arXiv 21 May 2025.

## Builds on (most cited first, 30 of 34)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [A Survey on the Memory Mechanism of Large Language Model based Agents](https://mlsanity.com/paper/2404.13501/) (2024)
- [API-Bank: A Comprehensive Benchmark for Tool-Augmented LLMs](https://mlsanity.com/paper/2304.08244/) (2023)
- [TravelPlanner: A Benchmark for Real-World Planning with Language Agents](https://mlsanity.com/paper/2402.01622/) (2024)
- [Large Language Models as Tool Makers](https://mlsanity.com/paper/2305.17126/) (2023)
- [EmbodiedBench: Comprehensive Benchmarking Multi-modal Large Language Models for Vision-Driven Embodied Agents](https://mlsanity.com/paper/2502.09560/) (2025)
- [Agent Q: Advanced Reasoning and Learning for Autonomous AI Agents](https://mlsanity.com/paper/2408.07199/) (2024)
- [LLaVA-Plus: Learning to Use Tools for Creating Multimodal Agents](https://mlsanity.com/paper/2311.05437/) (2023)
- [MultiAgentBench: Evaluating the Collaboration and Competition of LLM agents](https://mlsanity.com/paper/2503.01935/) (2025)
- [Rethinking the Bounds of LLM Reasoning: Are Multi-Agent Discussions the Key?](https://mlsanity.com/paper/2402.18272/) (2024)
- [CLIN: A Continually Learning Language Agent for Rapid Task Adaptation and Generalization](https://mlsanity.com/paper/2310.10134/) (2023)
- [GameBench: Evaluating Strategic Reasoning Abilities of LLM Agents](https://mlsanity.com/paper/2406.06613/) (2024)
- [Proactive Agent: Shifting LLM Agents from Reactive Responses to Active Assistance](https://mlsanity.com/paper/2410.12361/) (2024)
- [LegalAgentBench: Evaluating LLM Agents in Legal Domain](https://mlsanity.com/paper/2412.17259/) (2024)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [ReviewAgents: Bridging the Gap Between Human and AI-Generated Paper Reviews](https://mlsanity.com/paper/2503.08506/) (2025)
- [Investigate-Consolidate-Exploit: A General Strategy for Inter-Task Agent Self-Evolution](https://mlsanity.com/paper/2401.13996/) (2024)
- [AppBench: Planning of Multiple APIs from Various APPs for Complex User Instruction](https://mlsanity.com/paper/2410.19743/) (2024)
- [The Law of Knowledge Overshadowing: Towards Understanding, Predicting, and Preventing LLM Hallucination](https://mlsanity.com/paper/2502.16143/) (2025)
- [Can LLMs Master Math? Investigating Large Language Models on Math Stack Exchange](https://mlsanity.com/paper/2404.00344/) (2024)

## Built on by (most cited first, 5 of 5)

- [UserBench: An Interactive Gym Environment for User-Centric Agents](https://mlsanity.com/paper/2507.22034/) (2025)
- [ShortageSim: Simulating Drug Shortages under Information Asymmetry](https://mlsanity.com/paper/2509.01813/) (2025)
- [From Abstract to Contextual: What LLMs Still Cannot Do in Mathematics](https://mlsanity.com/paper/2601.23048/) (2026)
- [How Far Are We? Systematic Evaluation of LLMs vs. Human Experts in Mathematical Contest in Modeling](https://mlsanity.com/paper/2604.04791/) (2026)
- [StatABench: Dataset and Framework for Evaluating Statistical Analysis Capabilities of LLMs](https://mlsanity.com/paper/2606.22977/) (2026)

## Abstract (arXiv)

Recent progress in large language models (LLMs) has enabled substantial advances in solving mathematical problems. However, existing benchmarks often fail to reflect the complexity of real-world problems, which demand open-ended, interdisciplinary reasoning and integration of computational tools. To address this gap, we introduce ModelingBench, a novel benchmark featuring real-world-inspired, open-ended problems from math modeling competitions across diverse domains, ranging from urban traffic optimization to ecosystem resource planning. These tasks require translating natural language into formal mathematical formulations, applying appropriate tools, and producing structured, defensible reports. ModelingBench also supports multiple valid solutions, capturing the ambiguity and creativity of practical modeling. We also present ModelingAgent, a multi-agent framework that coordinates tool use, supports structured workflows, and enables iterative self-refinement to generate well-grounded, creative solutions. To evaluate outputs, we further propose ModelingJudge, an expert-in-the-loop system leveraging LLMs as domain-specialized judges assessing solutions from multiple expert perspectives. Empirical results show that ModelingAgent substantially outperforms strong baselines and often produces solutions indistinguishable from those of human experts. Together, our work provides a comprehensive framework for evaluating and advancing real-world problem-solving in open-ended, interdisciplinary modeling challenges.