ModelingAgent: Bridging LLMs and Mathematical Modeling for Real-World Challenges (2505.15068v1)

Abstract: Recent progress in 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.

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

This paper introduces an innovative framework, ModelingAgent, designed to enhance the problem-solving capabilities of LLMs in tackling real-world mathematical modeling challenges. Despite the advancements in LLMs regarding abstract mathematical problems, their application to complex, practical scenarios has remained limited. This research provides a structured approach to address this gap through ModelingBench, a benchmark inspired by real-world math modeling competitions, and a multi-agent system called ModelingAgent.

Overview

The paper identifies significant limitations in standard mathematical benchmarks that typically prioritize abstract and decontextualized problems. These benchmarks fail to capture the interdisciplinary reasoning and application of computational tools required for real-world challenges. For instance, solving problems such as urban traffic optimization or ecosystem resource planning demands an overview of natural language processing, mathematical formulations, and practical data integration. The authors introduce ModelingBench, a novel benchmark composed of diverse, open-ended problems that reflect real-world complexity. The benchmark encourages creativity and allows multiple valid solutions, presenting an authentic testbed for evaluating modeling capabilities.

At the core of the paper is the development of ModelingAgent, a multi-agent framework that coordinates the application of tools and supports structured workflows for generating well-grounded solutions. The system consists of four agents each specializing in distinct roles: Idea Proposer, Data Searcher, Modeling Implementor, and Report Writer. These agents collaborate within a shared memory space, iteratively refining their outputs for enhanced problem-solving effectiveness.

Key Elements

1. ModelingBench: This benchmark is carefully curated to challenge LLMs by incorporating tasks that require holistic understanding, flexible tool use, and creative modeling strategies. It spans domains such as sports analytics, financial modeling, biological systems, and operations management, thus fostering interdisciplinary approaches.
2. ModelingAgent: The multi-agent system is designed to mimic the collaborative dynamics seen in human problem-solving teams. The agents perform specialized functions such as decomposing tasks, searching for data, implementing models, and crafting reports. The framework integrates a Critic Module for continuous self-refinement, enhancing solution quality through iterative feedback.
3. ModelingJudge: To evaluate the outputs, the paper proposes ModelingJudge, an expert-in-the-loop system that leverages LLMs for domain-specialized assessments. This framework simulates real-world expert grading practices, providing a comprehensive evaluation from multiple expert perspectives.

Experimental Results

Empirical evaluations demonstrate that ModelingAgent significantly outperforms strong baselines, often producing solutions indistinguishable from human experts. It achieves up to a 20% improvement in performance metrics, although a gap of around 10% remains compared to award-winning human solutions. This highlights the room for improvement in the areas of structural coherence, solution completeness, and analytical depth. Notably, in human assessments, the outputs from the ModelingAgent successfully passed Turing tests over 50% of the time, confirming its ability to generate convincing, human-like solutions.

Implications

The research underscores the potential of LLMs to transcend traditional benchmarks and engage with practical, real-world challenges. The proposed framework effectively combines computational efficiency with creative problem-solving, suggesting pathways for future advancements in AI. As LLMs approach performance saturation on conventional tasks, ModelingAgent presents a fundamental shift towards more grounded, practical, and interpretable intelligence.

The framework also opens avenues for expanding LLM capabilities in interdisciplinary fields, potentially redefining intelligence evaluation metrics to better reflect problem-solving skills applicable to societal challenges. Further exploration could include integrating multi-modal reasoning and human-in-the-loop feedback to bridge existing performance gaps, enhance model reliability, and promote transparency and accountability in AI-driven decision-making.

The paper's contributions lay the groundwork for rethinking how AI's problem-solving potential is assessed, advocating for benchmarks and models that embrace the complexities of real-world applications.