MM-Agent: LLM as Agents for Real-world Mathematical Modeling Problem

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

SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains

Neural operators are efficient surrogate models for solving partial differential equations (PDEs), but their key components face challenges: (1) in order to improve accuracy, attention mechanisms suffer from computational inefficiency on large-scale meshes, and (2) spectral convolutions rely on the Fast Fourier Transform (FFT) on regular grids and assume a flat geometry, which causes accuracy degradation on irregular domains. To tackle these problems, we regard the matrix-vector operations in the standard attention mechanism on vectors in Euclidean space as bilinear forms and linear operators in vector spaces and generalize the attention mechanism to function spaces. This new attention mechanism is fully equivalent to the standard attention but impossible to compute due to the infinite dimensionality of function spaces. To address this, inspired by model reduction techniques, we propose a Subspace Parameterized Attention (SUPRA) neural operator, which approximates the attention mechanism within a finite-dimensional subspace. To construct a subspace on irregular domains for SUPRA, we propose using the Laplacian eigenfunctions, which naturally adapt to domains' geometry and guarantee the optimal approximation for smooth functions. Experiments show that the SUPRA neural operator reduces error rates by up to 33% on various PDE datasets while maintaining state-of-the-art computational efficiency.