MATHMO: Automated Mathematical Modeling Through Adaptive Search

Mathematical modeling is the process of understanding and predicting complex real-world phenomena. Traditionally, it is a time-intensive effort reliant on deep human expertise and iterative refinement. Automating this intricate process, therefore, offers the potential to significantly accelerate discovery and broaden the application of mathematical modeling across diverse domains. Such automation, however, must address inherent challenges, including fundamental modeling uncertainty, balancing multiple conflicting objectives, and incorporating subjective qualities into assessing model utility. We approach this by conceptualizing mathematical modeling as a sequential decision-making problem under uncertainty. In response, we introduce $\texttt{MATHMO}$, a novel adaptive search method designed to automatically navigate the complex decisions in selecting mathematical frameworks, specifying model formulations, and defining algorithmic procedures. Specifically, $\texttt{MATHMO}$ employs a principled bi-level search strategy---combining high-level exploration across diverse frameworks and local intra-framework model refinements---leveraging Large Language Models for exploration, surrogate evaluations, and incorporating subjective preferences into the automated process. We demonstrate $\texttt{MATHMO}$'s efficacy on diverse real-world tasks, where it successfully discovers Pareto-efficient frontiers of models that balance varied objectives, including subjective criteria.