Defining Foundation Models for Computational Science: A Call for Clarity and Rigor

This paper highlights the need for a clear, formal definition of foundation models in computational science, emphasizing core qualities like generality, reusability, and scalability. It introduces the Data-Driven Finite Element Method (DD-FEM), which combines traditional numerical methods with data-driven learning to address challenges such as scalability and physics consistency, providing a foundation for future development in the field.