M odeling A gent: Bridging LLM s and Mathematical Modeling for Real-World Challenges (2025)

Abstract: Recent progress in large language models (LLMs) has enabled substantial advances in solving mathematical problems. However, existing benchmarks often fail to reflect real-world complexity, 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 supports multiple valid solutions, capturing the ambiguity and creativity of practical modeling. To solve these challenges, we present **ModelingAgent**, a multi-agent framework that coordinates tool use, supports structured workflows, and enables iterative self-refinement to generate well-grounded, creative solutions. 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. All the codes are released for future research.

## introduction understanding and navigating the real world is a hallmark of human intelligence @xcite . at its core, intelligence is not merely about retrieving facts or manipulating symbols, but about perceiving complex, often ambiguous situations and making sound, goal-directed decisions. one of the most powerful tools humans have developed for this purpose is mathematics: not just 1 https://github.com/qiancheng0/modelingagent for abstract puzzles, but to structure messy, dynamic scenarios into analyzable forms @xcite . this process-mathematical modeling-is fundamental to human reasoning in science, economics, and policy-making. it involves translating real-world situations into formal mathematical representations, analyzing them, and interpreting the results to inform decisions. ## modelingbench historically rooted in practical necessity, mathematics has long served as a lens through which we interpret and navigate the world @xcite . modeling continues this by requiring not only computational competence but also creativity and domain knowledge. ## modelingagent to better tackle mathematical modeling problems, we draw inspiration from real-world competition teams, where participants with diverse expertise collaborate under a mentor's guidance. this motivates our multi-agent framework, emulating such problem-solving dynamics with llms. ## modelingjudge given the open-ended nature of tasks in model-ingbench, we propose modelingjudge, a multiexpert-in-the-loop evaluation framework simulating real-world modeling competitions. similar to mcm/icm, where rankings depend solely on report quality, modelingjudge assesses llm performance based on final reports that must comprehensively document the modeling process and address all task requirements. drawing from mcm's multijudge review system, our framework also incorporates diverse expert perspectives for balanced and robust evaluations, detailed in appendix e. ## experiments in this section, we present benchmarking results on modelingbench and evaluate the effectiveness of the modelingagent framework in addressing complex modeling problems. ## conclusion and future work our work introduces modelingbench, a math modeling benchmark bridging abstract mathematical reasoning with real-world problem-solving, and modelingagent, a multi-agent llm framework that supports complex modeling through structured collaboration, iterative refinement, and strategic tool use. our modelingjudge evaluation framework further enables real-world competition inspired, expert-aligned assessment. together, these contributions demonstrate the potential of llms to address practical challenges in multiple domains. despite clear improvements over baselines, mod-elingagent still faces challenges in creativity, data reliability, and domain adaptation, pointing to open questions and new opportunities for advancing llm-driven modeling in real-world contexts. future work could focus on expanding multimodal reasoning capabilities, enabling models to integrate visual, textual, and structured data essential for solving complex, real-world problems across domains like climate resilience, healthcare, and economic policy. additionally, advancing the agentic self-evolution framework with stronger causal reasoning and human-in-the-loop feedback is critical to improving solution reliability and fostering more accountable decision-making. we envision this work as a foundation for rethinking how we evaluate llms as their performance converges on standard benchmarks, and for inspiring new interdisciplinary methods that amplify real-world impact at the intersection of nlp, mathematical modeling, and high-stakes decision-making.