When we talk about foundation models, what are we talking about? This is a reflection piece on foundation models by drawing an analogy from numerical solutions in fluid dynamics.

This paper explore the challenges in building these models for science and engineering and introduce a promising framework called the Data-Driven Finite Element Method (DD-FEM), which aims to bridge traditional numerical methods with modern AI to provide a rigorous foundation for this exciting new field.

Choi, Y., Cheung, S. W., Kim, Y., Tsai, P. H., Diaz, A. N., Zanardi, I., ... & Heinkenschloss, M. (2025). Defining Foundation Models for Computational Science: A Call for Clarity and Rigor. arXiv preprint arXiv:2505.22904.