Automated physical model building from literature sources: Combining equations based on four predefined requirements

Constructing physical models from equations extracted from scientific literature databases is a challenging task due to the presence of redundant, intermediate, or inconsistent equations. This study formalizes model building as the combination of equations to form desired models that satisfy criteria such as input–output completeness and consistency. To address this problem, we propose a refined gradual method, an efficient algorithm that iteratively refines candidate equation groups while ensuring perfect recall and avoiding unnecessary computations. Evaluation of the proposed method on eight case studies, including noisy datasets, complex systems, and diverse equation structures, demonstrated that the refined gradual method reduced computational time compared to existing methods and successfully constructed all desired models. The study also identifies limitations of the proposed method and suggests improvements to enhance efficiency and adaptability. By providing a general framework for solving equation combination problems, this study advances automated model-building techniques and offers a robust approach for handling complex and noisy datasets in scientific and engineering disciplines.