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

TL;DR

This paper introduces ModelingBench, a new benchmark for real-world-inspired mathematical modeling problems, and ModelingAgent, a multi-agent framework that enhances LLMs' ability to solve complex, open-ended interdisciplinary challenges.

Contribution

The paper presents a novel benchmark and a multi-agent framework that improve LLMs' performance on real-world mathematical modeling tasks, supporting open-ended problem-solving and expert evaluation.

Findings

ModelingAgent outperforms strong baselines.

Solutions often match human expert quality.

Framework effectively evaluates interdisciplinary modeling solutions.

Abstract

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.